Novel conditions for finite time stability of discrete time delay systems (original) (raw)
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The stability of linear discrete time delay systems over a finite time interval: New results
Proceedings of the 10th World Congress on Intelligent Control and Automation, 2012
This paper gives sufficient conditions for the practical and finite time stability of a particular class of linear discrete time delay systems. Analyzing the finite time stability concept, these new delay-independent conditions are derived using an approach based on the Lyapunov-like functions. The practical and attractive practical stability for discrete time delay systems has been investigated. The above mentioned approach was supported by the classical Lyapunov technique to guarantee the attractivity properties of the system behavior.
2011 9th IEEE International Conference on Control and Automation (ICCA), 2011
ABSTRACT This paper gives sufficient conditions for the practical and finite time stability of a particular class of linear discrete time delay systems. Analyzing the finite time stability concept, these new delay-independent conditions are derived using an approach based on the Lyapunov-like functions. The practical stability and attractive practical stability for discrete time delay systems have been investigated. The above mentioned approach was supported by the classical Lyapunov technique to guarantee the attractivity properties of the system behavior.
Further Results on Finite Timeand Practical Stability of Linear Continuous Time Delay Systems
In this paper, finite-time stability and practical stability problems for a class of linear continuous time-delay systems are studied. Based on the Lyapunov-like functions, that do not have to be positive definite in the whole state space and not need to have negative definite derivatives along the system trajectories, the new sufficient finite-time stability conditions are obtained. To obtain the conditions for attractive practical stability, the mentioned approach is combined with classical Lyapunov technique to guarantee attractivity properties of system behavior, and new delay dependent sufficient condition has been derived. The described approach was compared with some previous methods and it has been showed that the results derived are commonly adequate but easier for numerical treatment.
Finite time stability of continuous time delay systems: Jensen's inequality-based approach
2014 9th IEEE Conference on Industrial Electronics and Applications, 2014
In this study, finite-time stability of the linear continuous time-delay systems was investigated. A novel formulation of the Lyapunov-like function was used to develop a new sufficient delay-dependent condition for finite-time stability. The proposed function does not need to be positive-definite in the whole state space, and it does not need to have negative derivatives along the system trajectories. The proposed method was compared with the previously developed and reported methodologies. It was concluded that the stability investigation using the novel condition for stability investigation was less complicated for numerical calculations. Furthermore, it gives comparable results in comparison with the ones obtained with other analyzed conditions, and it provides superior results for some systems.
An efficient method for finite time stability calculation of continuous time delay systems
2013 9th Asian Control Conference (ASCC), 2013
This paper provides sufficient conditions for the finite time stability of linear continuous time delay systems mathematically described as x , (t)=A 0 x(t) + A 1 x(t-τ). A novel method was used to derive new delay dependent conditions. The conditions obtained were applied in the system stability analysis. Consequently, the aggregation function does not have to be positive in the state space domain, and does not need to have the negative derivatives along the system trajectories. Finite time stability was analyzed using the novel conditions derived in the paper. The described approach was compared with some known methods. It was proved that the new results were in compliance with the previously reported results, but more convenient for numerical calculations. The numerical example was presented to support the results.
Delay-Dependent Conditions for Finite Time Stability of Continuous Systems with Latency
2013
In the present study, the practical and finite time stability of linear continuous system with latency has been investigated. The proposed result outlines the novel sufficient stability conditions for the systems represented by the following equation: x(t)=A 0 x(t) -A 1 x(t -). The results can be applied to the analysis of both the practical and finite time stability of the continuous systems with time delay. For the derivation of the finite time stability conditions, the Lyapunov-Krassovski functionals were used. Unlike in the previously reported results, the functionals did not have to satisfy some strict mathematical conditions, such as positivity in the whole state space and possession of the negative derivatives along the system state trajectories. The numerical examples presented in this study additionally clarified the implementation of the methodology, and the calculations of the stability conditions. Generally, it was found that the proposed sufficient conditions were less restrictive compared to the ones previously reported.
Discrete Dynamics in Nature and Society, 2015
The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature.
On finite time instability of continuous time delay systems
2014 9th IEEE Conference on Industrial Electronics and Applications, 2014
Finite time instability for linear continuous timedelay systems was investigated in this paper. The novel Lyapunov-like functions were used in the analysis. The functions do not need to fulfill the following conditions: being positive definite on the whole state space domain and possessing negative derivatives along the system trajectories. These functions were previously used for the development of both the delay-dependent and delay-independent sufficient conditions for the investigation of the finite time stability of control systems. However, the reported conditions cannot be used for the precise calculation of the instant when the system trajectory leaves the prescribed boundaries. In this paper, a novel concept of finite time instability was introduced to solve this problem. Numerical examples were used to additionally clarify the procedure.
Comments on finite-time stability of time-delay systems
Automatica, 2014
Recently proposed conditions on finite-time stability in time-delay systems are revisited and it is shown that they are incorrect. General comments on possibility of finite-time convergence in time-delay systems and a necessary condition are given.