Muzaffer ATEŞ - Academia.edu (original) (raw)
Papers by Muzaffer ATEŞ
International Journal of Optimization and Control : Theories & Applications, Jul 31, 2021
In this paper, the global asymptotic stability and strong passivity of three types of nonlinear L... more In this paper, the global asymptotic stability and strong passivity of three types of nonlinear LRC circuits are investigated by utilizing the Lyapunov's direct method. The stability conditions are obtained by constructing appropriate energy (or Lyapunov) function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. Many specialists construct Lyapunov functions by using some properties of the functions with much trial and errors or for a system they choose candidate Lyapunov functions. So, for a given system the Lyapunov function is not unique. But we insist that the Lyapunov (energy) function is unique for a given physical system. Thus, this study clarifies Lyapunov stability with suitable tools and also improves some previous studies. Our approach is constructing energy function for a given nonlinear system that based on the power-energy relationship of the system. Hence for a dynamical system, the derivative of the Lyapunov function is equal to the negative value of the dissipative power in the system. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The provided results are central importance for the stability analysis of nonlinear systems. Some simulation results are also given successfully that verify the theoretical predictions.
Nonlinear Dynamics, Jun 15, 2006
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Journal of the Indonesian Mathematical Society, May 3, 2016
This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic so... more This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic solutions for a class of nonlinear vector differential equations of fifth order. With this work, we extend and improve two related results in the literature from scalar cases to vectorial cases. An example is given to illustrate the theoretical analysis made in this paper.
New trends in mathematical sciences, Jul 1, 2022
Series and parallel LRC circuit systems are widely encountered in numerous electrical, electronic... more Series and parallel LRC circuit systems are widely encountered in numerous electrical, electronics, control issues and differential equation applications. Accurate control of the current in series and voltage in parallel LRC circuit systems with nonlinear time-varying inductance, resistance and capacitance is a challenge. In this study, a novel approach proposed for control of current in nonlinear time-varying series LRC circuit and voltage in nonlinear and time-varying parallel LRC circuit. The proposed controller is characterized by a nonlinear algebraic equation and straining the tracking error converge to zero. Illustrative results confirm the proposed approach for forcing the current /voltage in series and parallel nonlinear time-varying LRC circuit to follow the targeted current /voltage trajectories efficiently. The proposed approach shows great novelty to determine the dynamics behavior of nonlinear time-varying systems. Therefore, the obtained results generalize and improve the existing conclusions. Simulations illustrate the feasibility and validity of the theoretical results.
International Journal of Circuit Theory and Applications, Nov 3, 2021
In this paper, we address the problem of global asymptotic stability and strong passivity analysi... more In this paper, we address the problem of global asymptotic stability and strong passivity analysis of nonlinear time‐varying systems controlled by a second‐order vector differential equation. First, we obtain this equation from a nonlinear time varying network of the circuit theory. Then, we construct the Lyapunov candidate function directly from the physical meaning of the given system. By the way, we review a number of previous results from the point view of Lyapunov's direct method. Our system with its real energy function generalize and improve upon some well‐known studies. The new concept facilitates the formulation of the energy (Lyapunov) function from the power‐energy relationship of the given system. Then, we also realized that the time derivative of the Lyapunov function for a given dynamical systems is the negative value of the power dissipated in the system. Therefore, with the proposed approach, one can inspect the result of the time derivative of the energy function for a given physical system. Finally, two examples (one with simulations) are used to illustrate the superiority and validity of the obtained results.
Discrete Dynamics in Nature and Society, 2013
This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth... more This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.
DergiPark (Istanbul University), Jan 4, 2022
Today, the qualitative behavior of dynamical systems is a very important subject of control theor... more Today, the qualitative behavior of dynamical systems is a very important subject of control theory. Based on this, we consider the stability and instability properties of the equilibrium points of Chua's circuit under suitable conditions by the Lyapunov direct method. This method gives us qualitative information directly without solving the given systems. From this circuit, we construct suitable energy or candidate Lyapunov function and then apply the method as a tool to investigate the global asymptotic stability and instability of the system. We also determine under which conditions the system behaves as a chaotic system or a memristor. In this study, we realized that an unforced dissipative dynamical system with bounded initial states has zero solution or motion at infinity. Some simulation results and examples are given to verify the obtained theoretical predictions.
arXiv (Cornell University), Aug 19, 2011
. Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions.... more . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite general third- order nonlinear vector differential equation, and one example is given for illustration of the subject.
International journal of mathematics and computer research, Apr 29, 2023
We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous diff... more We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous differential equation. We prove that the solutions of this equation are bounded by Cauchy formula.
Zenodo (CERN European Organization for Nuclear Research), Apr 27, 2023
We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous diff... more We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous differential equation. We prove that the solutions of this equation are bounded by Cauchy formula.
International Journal of Circuit Theory and Applications
SummaryThis paper discusses the global asymptotic stability and strong passivity analysis of four... more SummaryThis paper discusses the global asymptotic stability and strong passivity analysis of fourth‐order nonlinear and time‐varying dynamical systems by utilizing the Lyapunov direct method. The mathematical model of the main system is obtained from a non‐linear and aging RLC circuit that we have designed before. RLC circuits play an excellent role in the stability of modern system theory. Without the concept of storage elements, the construction of Lyapunov or energy functions for nonlinear and time‐varying systems may be difficult. Because of this, although there are many studies on the stability concept, but the subject has not been completed yet. Therefore, this study may present some mathematical technicalities to the Lyapunov stability with physical considerations. The Lyapunov functions obtained from RLC circuits are natural storage functions, and they satisfy the dissipation inequality. The theoretical stability results of the system are also discussed by Lyapunov's lin...
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH
We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous diff... more We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous differential equation. We prove that the solutions of this equation are bounded byCauchy formula
arXiv: Classical Analysis and ODEs, Aug 19, 2011
An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
In this paper, the global asymptotic stability and strict passivity of three types of nonlinear R... more In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These...
International Journal of Circuit Theory and Applications, 2021
In this paper, we address the problem of global asymptotic stability and strong passivity analysi... more In this paper, we address the problem of global asymptotic stability and strong passivity analysis of nonlinear and nonautonomous systems controlled by second-order vector differential equations. First, we construct this system or the differential equation from a nonlinear time varying network of the circuit theory. Our system and with its real energy function generalize and improve upon some well-known studies in the literature. This system and its special forms have ample applications in many scientific investigations. We realized that most of the first- and second-order ordinary differential equations can be represented by LRC circuits. So, the energy (Lyapunov) functions of the systems can be constructed directly without much trial and error. By this way, the application of Lyapunov’s direct method may become a standard technique for physical systems. We illuminate this idea with many applications and improvements. We also compare the Lyapunov stability theory with Hamiltonian and Lagrangian systems in the sense of conservative and dissipative systems. Then, we provide new explicit stability and passivity results with minimum criteria.
We studied the stability and boundedness results of a third-order nonlinear and nonautonomous dif... more We studied the stability and boundedness results of a third-order nonlinear and nonautonomous differential equations of the form . 0 , , , , , , x x x t f x x x x t x Generally particular cases of autonomous form and some particular cases of nonautonomous form of this equation have been studied by many authors over the years. However, this particular form is a generalization of the earlier ones. A suitable Lyapunov function was constructed and used for the proof of the main theorem. The results in the paper generalize other authors who have studied particular cases of the differential equations. Finally, a concrete example is given to check our results.
TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES, 2018
This paper deals with the global asymptotic stability (GAS) of certain nonlinear RLC circuit syst... more This paper deals with the global asymptotic stability (GAS) of certain nonlinear RLC circuit systems using the direct Lyapunov method. For each system a suitable Lyapunov function or energy-like function is constructed and the direct Lyapunov method is applied to the related system. Then the invariant equilibrium point of each system that makes the system solution to the global asymptotic stable is determined. Some new explicit GAS conditions of certain nonlinear RLC circuit systems are derived by Lyapunov's direct method. The presented simulations are compatible with the new results. The results are given with proofs.
Journal of the Indonesian Mathematical Society
This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic so... more This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic solutions for a class of nonlinear vector differential equations of fifth order. With this work, we extend and improve two related results in the literature from scalar cases to vectorial cases. An example is given to illustrate the theoretical analysis made in this paper.
Journal of Applied Mathematics, 2013
We studied the global stability and boundedness results of third-order nonlinear differential equ... more We studied the global stability and boundedness results of third-order nonlinear differential equations of the form . Particular cases of this equation have been studied by many authors over years. However, this particular form is a generalization of the earlier ones. A Lyapunov function was used for the proofs of the two main theorems: one with and the other with . The results in this paper generalize those of other authors who have studied particular cases of the differential equations. Finally, a concrete example is given to check our results.
International Journal of Optimization and Control : Theories & Applications, Jul 31, 2021
In this paper, the global asymptotic stability and strong passivity of three types of nonlinear L... more In this paper, the global asymptotic stability and strong passivity of three types of nonlinear LRC circuits are investigated by utilizing the Lyapunov's direct method. The stability conditions are obtained by constructing appropriate energy (or Lyapunov) function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. Many specialists construct Lyapunov functions by using some properties of the functions with much trial and errors or for a system they choose candidate Lyapunov functions. So, for a given system the Lyapunov function is not unique. But we insist that the Lyapunov (energy) function is unique for a given physical system. Thus, this study clarifies Lyapunov stability with suitable tools and also improves some previous studies. Our approach is constructing energy function for a given nonlinear system that based on the power-energy relationship of the system. Hence for a dynamical system, the derivative of the Lyapunov function is equal to the negative value of the dissipative power in the system. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The provided results are central importance for the stability analysis of nonlinear systems. Some simulation results are also given successfully that verify the theoretical predictions.
Nonlinear Dynamics, Jun 15, 2006
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Journal of the Indonesian Mathematical Society, May 3, 2016
This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic so... more This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic solutions for a class of nonlinear vector differential equations of fifth order. With this work, we extend and improve two related results in the literature from scalar cases to vectorial cases. An example is given to illustrate the theoretical analysis made in this paper.
New trends in mathematical sciences, Jul 1, 2022
Series and parallel LRC circuit systems are widely encountered in numerous electrical, electronic... more Series and parallel LRC circuit systems are widely encountered in numerous electrical, electronics, control issues and differential equation applications. Accurate control of the current in series and voltage in parallel LRC circuit systems with nonlinear time-varying inductance, resistance and capacitance is a challenge. In this study, a novel approach proposed for control of current in nonlinear time-varying series LRC circuit and voltage in nonlinear and time-varying parallel LRC circuit. The proposed controller is characterized by a nonlinear algebraic equation and straining the tracking error converge to zero. Illustrative results confirm the proposed approach for forcing the current /voltage in series and parallel nonlinear time-varying LRC circuit to follow the targeted current /voltage trajectories efficiently. The proposed approach shows great novelty to determine the dynamics behavior of nonlinear time-varying systems. Therefore, the obtained results generalize and improve the existing conclusions. Simulations illustrate the feasibility and validity of the theoretical results.
International Journal of Circuit Theory and Applications, Nov 3, 2021
In this paper, we address the problem of global asymptotic stability and strong passivity analysi... more In this paper, we address the problem of global asymptotic stability and strong passivity analysis of nonlinear time‐varying systems controlled by a second‐order vector differential equation. First, we obtain this equation from a nonlinear time varying network of the circuit theory. Then, we construct the Lyapunov candidate function directly from the physical meaning of the given system. By the way, we review a number of previous results from the point view of Lyapunov's direct method. Our system with its real energy function generalize and improve upon some well‐known studies. The new concept facilitates the formulation of the energy (Lyapunov) function from the power‐energy relationship of the given system. Then, we also realized that the time derivative of the Lyapunov function for a given dynamical systems is the negative value of the power dissipated in the system. Therefore, with the proposed approach, one can inspect the result of the time derivative of the energy function for a given physical system. Finally, two examples (one with simulations) are used to illustrate the superiority and validity of the obtained results.
Discrete Dynamics in Nature and Society, 2013
This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth... more This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.
DergiPark (Istanbul University), Jan 4, 2022
Today, the qualitative behavior of dynamical systems is a very important subject of control theor... more Today, the qualitative behavior of dynamical systems is a very important subject of control theory. Based on this, we consider the stability and instability properties of the equilibrium points of Chua's circuit under suitable conditions by the Lyapunov direct method. This method gives us qualitative information directly without solving the given systems. From this circuit, we construct suitable energy or candidate Lyapunov function and then apply the method as a tool to investigate the global asymptotic stability and instability of the system. We also determine under which conditions the system behaves as a chaotic system or a memristor. In this study, we realized that an unforced dissipative dynamical system with bounded initial states has zero solution or motion at infinity. Some simulation results and examples are given to verify the obtained theoretical predictions.
arXiv (Cornell University), Aug 19, 2011
. Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions.... more . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite general third- order nonlinear vector differential equation, and one example is given for illustration of the subject.
International journal of mathematics and computer research, Apr 29, 2023
We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous diff... more We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous differential equation. We prove that the solutions of this equation are bounded by Cauchy formula.
Zenodo (CERN European Organization for Nuclear Research), Apr 27, 2023
We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous diff... more We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous differential equation. We prove that the solutions of this equation are bounded by Cauchy formula.
International Journal of Circuit Theory and Applications
SummaryThis paper discusses the global asymptotic stability and strong passivity analysis of four... more SummaryThis paper discusses the global asymptotic stability and strong passivity analysis of fourth‐order nonlinear and time‐varying dynamical systems by utilizing the Lyapunov direct method. The mathematical model of the main system is obtained from a non‐linear and aging RLC circuit that we have designed before. RLC circuits play an excellent role in the stability of modern system theory. Without the concept of storage elements, the construction of Lyapunov or energy functions for nonlinear and time‐varying systems may be difficult. Because of this, although there are many studies on the stability concept, but the subject has not been completed yet. Therefore, this study may present some mathematical technicalities to the Lyapunov stability with physical considerations. The Lyapunov functions obtained from RLC circuits are natural storage functions, and they satisfy the dissipation inequality. The theoretical stability results of the system are also discussed by Lyapunov's lin...
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH
We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous diff... more We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous differential equation. We prove that the solutions of this equation are bounded byCauchy formula
arXiv: Classical Analysis and ODEs, Aug 19, 2011
An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
In this paper, the global asymptotic stability and strict passivity of three types of nonlinear R... more In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These...
International Journal of Circuit Theory and Applications, 2021
In this paper, we address the problem of global asymptotic stability and strong passivity analysi... more In this paper, we address the problem of global asymptotic stability and strong passivity analysis of nonlinear and nonautonomous systems controlled by second-order vector differential equations. First, we construct this system or the differential equation from a nonlinear time varying network of the circuit theory. Our system and with its real energy function generalize and improve upon some well-known studies in the literature. This system and its special forms have ample applications in many scientific investigations. We realized that most of the first- and second-order ordinary differential equations can be represented by LRC circuits. So, the energy (Lyapunov) functions of the systems can be constructed directly without much trial and error. By this way, the application of Lyapunov’s direct method may become a standard technique for physical systems. We illuminate this idea with many applications and improvements. We also compare the Lyapunov stability theory with Hamiltonian and Lagrangian systems in the sense of conservative and dissipative systems. Then, we provide new explicit stability and passivity results with minimum criteria.
We studied the stability and boundedness results of a third-order nonlinear and nonautonomous dif... more We studied the stability and boundedness results of a third-order nonlinear and nonautonomous differential equations of the form . 0 , , , , , , x x x t f x x x x t x Generally particular cases of autonomous form and some particular cases of nonautonomous form of this equation have been studied by many authors over the years. However, this particular form is a generalization of the earlier ones. A suitable Lyapunov function was constructed and used for the proof of the main theorem. The results in the paper generalize other authors who have studied particular cases of the differential equations. Finally, a concrete example is given to check our results.
TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES, 2018
This paper deals with the global asymptotic stability (GAS) of certain nonlinear RLC circuit syst... more This paper deals with the global asymptotic stability (GAS) of certain nonlinear RLC circuit systems using the direct Lyapunov method. For each system a suitable Lyapunov function or energy-like function is constructed and the direct Lyapunov method is applied to the related system. Then the invariant equilibrium point of each system that makes the system solution to the global asymptotic stable is determined. Some new explicit GAS conditions of certain nonlinear RLC circuit systems are derived by Lyapunov's direct method. The presented simulations are compatible with the new results. The results are given with proofs.
Journal of the Indonesian Mathematical Society
This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic so... more This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic solutions for a class of nonlinear vector differential equations of fifth order. With this work, we extend and improve two related results in the literature from scalar cases to vectorial cases. An example is given to illustrate the theoretical analysis made in this paper.
Journal of Applied Mathematics, 2013
We studied the global stability and boundedness results of third-order nonlinear differential equ... more We studied the global stability and boundedness results of third-order nonlinear differential equations of the form . Particular cases of this equation have been studied by many authors over years. However, this particular form is a generalization of the earlier ones. A Lyapunov function was used for the proofs of the two main theorems: one with and the other with . The results in this paper generalize those of other authors who have studied particular cases of the differential equations. Finally, a concrete example is given to check our results.