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Papers by Mihaela-hanako Matcovschi

Research paper thumbnail of Timed Continuous Petri Nets: Set Invariance in Feedback Design for Componentwise Boundedness and Weak Conservativity

This paper depicts a method for ensuring refined boundedness properties, namely componentwise bou... more This paper depicts a method for ensuring refined boundedness properties, namely componentwise boundedness and weak conservativity, for timed continuous Petri nets operating with infinite server semantics. The theoretical foundation, based on set-invariance, is followed by the presentation of the numerical implementation as a linear programming problem. A case study illustrates the applicability of our approach.

Research paper thumbnail of Boundedness properties of timed continuous Petri nets with interval firing rates

ABSTRACT This paper presents the concepts of d-upper boundedness and weakly δ-conservativeness fo... more ABSTRACT This paper presents the concepts of d-upper boundedness and weakly δ-conservativeness for general Timed Continuous Petri nets. The analysis is extended to the case when the exact values of the firing rates of the transitions are uncertain, but the intervals of their values are known (the firing rates are constant, between prescribed minimal and maximal values). The example of a manufacturing system is included in order to illustrate these concepts.

Research paper thumbnail of On the boundedness of timed continuous Petri nets

ABSTRACT For a timed continuous Petri net (TCPN), the paper introduces a new concept of boundedne... more ABSTRACT For a timed continuous Petri net (TCPN), the paper introduces a new concept of boundedness based on the existence of (positive) invariant sets with respect to the marking of the net, sets that are defined by weighted Hölder p-norms. For join-free TCPNs, this type of boundedness is characterized by inequalities satisfied by the measure of the matrix that defines the dynamics of the marking. Some connections with the structural properties of the net topology are also delivered.

Research paper thumbnail of EXPLICIT SOLUTIONS TO SOME VECTORIAL DIFFERENTIAL EQUATIONS I. General Results

Bul. Inst. Polit. Iasi. 04/2001; XLVII (LI)(1-2, s.I,. 2001):pp. 303-313..

The aim of this paper is to present a procedure that allows to point out the vectorial solutions... more The aim of this paper is to present a procedure that allows
to point out the vectorial solutions to some Cauchy problems not depicted in any dynamics treatise yet. The main results are presented in Theorems 3 and 4 and show the explicit form of these solutions.

Research paper thumbnail of Flow-invariance and stability analysis for a class of nonlinear systems with slope conditions

New results of qualitative analysis are presented for a class of dynamical systems (including the... more New results of qualitative analysis are presented for a class of dynamical systems (including the Hopfield neural networks) whose nonlinearities satisfy certain slope conditions. The main instrument of this analysis consists in the individual monitoring of the statetrajectories by considering time-dependent rectangular sets that are forward invariant with respect to the dynamics of the investigated systems. Particular requirements for the rectangular sets approaching the equilibrium point allow a componentwise exploration of the stability properties, offering additional information with respect to the traditional framework (that expresses a global knowledge, built in terms of norms). Within this context, we are able to point out some important dynamical aspects that remained hidden for other works relying only on the standard tools of stability analysis. The refinement induced by the componentwise point of view is also revealed by two numerical examples.

Research paper thumbnail of Diagonal stability of interval matrices and applications

P is a positive definite diagonal matrix and the notation "≺ 0" means negative definite. The firs... more P is a positive definite diagonal matrix and the notation "≺ 0" means negative definite. The first part of the paper • provides SDS p and HDS p criteria, • presents methods for finding the positive definite diagonal matrix requested by the definition of SDS p and HDS p , • analyzes the robustness of SDS p and HDS p and • explores the connection with the Schur and Hurwitz stability of A I . The second part shows that the SDS p or HDS p of A I is equivalent to the following properties of a discrete-or continuous-time dynamical interval system whose motion is described by A I : • the existence of a strong Lyapunov function defined by the p-norm and • the existence of exponentially decreasing sets defined by the p-norm that are invariant with respect to system's trajectories.

Research paper thumbnail of SYMBOLIC REPRESENTATION OF CONTINUAL AND DISCRETE SIGNALS ON FINITE ORDER ALGEBRAS

This paper presents the two basic problems related to symbolic representations of finite dimensio... more This paper presents the two basic problems related to symbolic representations of finite dimensional R -linear spaces endowed with an endomorphism on finite order R -algebras. In particular, the symbolic representations of either continual signals that are solutions to linear differential equations or discrete signals representing solutions to difference equations, are obtained. The symbolic representation introduced in this paper allows an unitary handling of the responses of both continual and discrete dynamical linear systems and generalises the classical frequency methods.

Research paper thumbnail of ON THE n-ORDER ACCELERATIONS DISTRIBUTION DURING RIGID MOTION

The properties of the n-order accelerations distribution of a rigid body under general motion are... more The properties of the n-order accelerations distribution of a rigid body under general motion are systematically studied based on tensor algebra. A tensor represents an R -linear mapping of the R -linear space of free vectors V into V . It may be represented by a matrix only after a basis in V was selected. Preferring an orthonormal basis simplifies the calculus, but this particular choice may conceal some essential properties. This paper uses the notion of rigid basis associated to a spherical rigid motion in order to point out some properties of the n-order accelerations tensor.

Research paper thumbnail of Computation of angular velocity and acceleration tensors by direct measurements

Acta Mechanica, 2002

The present paper investigates the properties of the angular velocity tensor ϕ and the angular ac... more The present paper investigates the properties of the angular velocity tensor ϕ and the angular acceleration tensor Ψ for rigid body motion. Three vectorial invariants of rigid body kinematics are presented. In case of tensor Ψ being non-singular, its inverse Ψ−1 is inferred. A novel procedure for automatic computation of tensor ϕ and Ψ based on measured velocity and acceleration data is developed. Depending of the type of available data, three algorithms are suggested. Numerical examples show the application of the method.

Research paper thumbnail of Algebraic computation of the twist of a rigid body through direct measurements

Computer Methods in Applied Mechanics and Engineering, 2001

The aim of the paper is to present a procedure for the automatic computation of the twist of a ri... more The aim of the paper is to present a procedure for the automatic computation of the twist of a rigid body and of its derivative with respect to time. This procedure is done through direct measurements, based on the velocities and accelerations of three non-collinear points of the rigid body. Firstly, the case of a rigid body in spherical motion is considered. Next, the case of the general motion is studied. Two algorithms for the algebraic computation of the twist of a rigid body and its derivative are further presented. Finally, an example is delivered.

Research paper thumbnail of Componentwise Stabilization of Interval Systems

Proceedings of the 17th IFAC World Congress, 2008, 2008

The componentwise stability of a linear system is a special type of asymptotic stability induced ... more The componentwise stability of a linear system is a special type of asymptotic stability induced by the existence of exponentially decreasing rectangular sets that are invariant with respect to the free response. An interval system ( )

Research paper thumbnail of Diagonally-invariant exponential stability

Proceedings of the 16th IFAC World Congress, 2005, 2005

... system (1). ∎ 3. DIESP AND MATRIX MEASURES Given a square matrix Q, consider its measure || |... more ... system (1). ∎ 3. DIESP AND MATRIX MEASURES Given a square matrix Q, consider its measure || || 0 ( ) lim(|| || 1)/ D p D p Q I Q θ µ θ θ ↓ = + − (8) associated with the matrix norm p D p QD D Q || || | 1 − = . Using the material ...

Research paper thumbnail of Qualitative Analysis Results for Arbitrarily Switching Positive Systems

Proceedings of the 18th IFAC World Congress, 2011

Research paper thumbnail of Symbolic Representation of Continual and Discrete Signals on Finite Order Algebras

This paper presents the two basic problems related to symbolic representations of finite dimensio... more This paper presents the two basic problems related to symbolic representations of finite dimensional R -linear spaces endowed with an endomorphism on finite order R -algebras. In particular, the symbolic representations of either continual signals that are solutions to linear differential equations or discrete signals representing solutions to difference equations, are obtained. The symbolic representation introduced in this paper allows an unitary handling of the responses of both continual and discrete dynamical linear systems and generalises the classical frequency methods.

Research paper thumbnail of New Results in the State-Space Analysis of Positive Linear Systems

Research paper thumbnail of Majorant Matrices in the Qualitative Analysis of Interval Dynamical Systems

Research paper thumbnail of Lyapunov functions and Lyapunov inequalities defined by Hölder p-norms for linear time-variant systems

Research paper thumbnail of Flow-Invariant Sets with Respect to the Markings of Timed Continuous Petri Nets

Proceedings of the 44th IEEE Conference on Decision and Control, 2005

The paper investigates the existence of flowinvariant sets with respect to the marking of a timed... more The paper investigates the existence of flowinvariant sets with respect to the marking of a timed continuous Petri net (TCPN) with infinite server semantics. Such a set has the property that for any initial marking belonging to the set, the marking at any moment in the evolution of the net also belongs to the set. Thus, the traditional concept of marking invariance used in PN theory, which refers to a set of places, is complemented in the sharper sense of the individual monitoring of each place. We take into consideration several types of bounded flow-invariant sets. The join-free TCPNs are treated separately from TCPNs with joins as allowing the development of supplementary investigation tools. Subsidiary to our results we give a consistent and rigorous mathematical proof for the nonnegativeness of the marking in TCPNs.

Research paper thumbnail of Matrix framework for analysis of invariant sets

International Symposium on Signals, Circuits and Systems, 2005. ISSCS 2005., 2005

For a large class of nonlinear dynamical systems, we provide results that allow testing the exist... more For a large class of nonlinear dynamical systems, we provide results that allow testing the existence of invariant sets with respect to the state space trajectories. These sets are considered as depending on time, in order to ensure the generality of the approach. The results operate as sufficient conditions formulated in terms of matrix measures associated with induced matrix norms.

Research paper thumbnail of On a conjecture in stability analysis of polytopic systems — Mimicking spectral radius properties from real to complex matrices

2014 18th International Conference on System Theory, Control and Computing (ICSTCC), 2014

Research paper thumbnail of Timed Continuous Petri Nets: Set Invariance in Feedback Design for Componentwise Boundedness and Weak Conservativity

This paper depicts a method for ensuring refined boundedness properties, namely componentwise bou... more This paper depicts a method for ensuring refined boundedness properties, namely componentwise boundedness and weak conservativity, for timed continuous Petri nets operating with infinite server semantics. The theoretical foundation, based on set-invariance, is followed by the presentation of the numerical implementation as a linear programming problem. A case study illustrates the applicability of our approach.

Research paper thumbnail of Boundedness properties of timed continuous Petri nets with interval firing rates

ABSTRACT This paper presents the concepts of d-upper boundedness and weakly δ-conservativeness fo... more ABSTRACT This paper presents the concepts of d-upper boundedness and weakly δ-conservativeness for general Timed Continuous Petri nets. The analysis is extended to the case when the exact values of the firing rates of the transitions are uncertain, but the intervals of their values are known (the firing rates are constant, between prescribed minimal and maximal values). The example of a manufacturing system is included in order to illustrate these concepts.

Research paper thumbnail of On the boundedness of timed continuous Petri nets

ABSTRACT For a timed continuous Petri net (TCPN), the paper introduces a new concept of boundedne... more ABSTRACT For a timed continuous Petri net (TCPN), the paper introduces a new concept of boundedness based on the existence of (positive) invariant sets with respect to the marking of the net, sets that are defined by weighted Hölder p-norms. For join-free TCPNs, this type of boundedness is characterized by inequalities satisfied by the measure of the matrix that defines the dynamics of the marking. Some connections with the structural properties of the net topology are also delivered.

Research paper thumbnail of EXPLICIT SOLUTIONS TO SOME VECTORIAL DIFFERENTIAL EQUATIONS I. General Results

Bul. Inst. Polit. Iasi. 04/2001; XLVII (LI)(1-2, s.I,. 2001):pp. 303-313..

The aim of this paper is to present a procedure that allows to point out the vectorial solutions... more The aim of this paper is to present a procedure that allows
to point out the vectorial solutions to some Cauchy problems not depicted in any dynamics treatise yet. The main results are presented in Theorems 3 and 4 and show the explicit form of these solutions.

Research paper thumbnail of Flow-invariance and stability analysis for a class of nonlinear systems with slope conditions

New results of qualitative analysis are presented for a class of dynamical systems (including the... more New results of qualitative analysis are presented for a class of dynamical systems (including the Hopfield neural networks) whose nonlinearities satisfy certain slope conditions. The main instrument of this analysis consists in the individual monitoring of the statetrajectories by considering time-dependent rectangular sets that are forward invariant with respect to the dynamics of the investigated systems. Particular requirements for the rectangular sets approaching the equilibrium point allow a componentwise exploration of the stability properties, offering additional information with respect to the traditional framework (that expresses a global knowledge, built in terms of norms). Within this context, we are able to point out some important dynamical aspects that remained hidden for other works relying only on the standard tools of stability analysis. The refinement induced by the componentwise point of view is also revealed by two numerical examples.

Research paper thumbnail of Diagonal stability of interval matrices and applications

P is a positive definite diagonal matrix and the notation "≺ 0" means negative definite. The firs... more P is a positive definite diagonal matrix and the notation "≺ 0" means negative definite. The first part of the paper • provides SDS p and HDS p criteria, • presents methods for finding the positive definite diagonal matrix requested by the definition of SDS p and HDS p , • analyzes the robustness of SDS p and HDS p and • explores the connection with the Schur and Hurwitz stability of A I . The second part shows that the SDS p or HDS p of A I is equivalent to the following properties of a discrete-or continuous-time dynamical interval system whose motion is described by A I : • the existence of a strong Lyapunov function defined by the p-norm and • the existence of exponentially decreasing sets defined by the p-norm that are invariant with respect to system's trajectories.

Research paper thumbnail of SYMBOLIC REPRESENTATION OF CONTINUAL AND DISCRETE SIGNALS ON FINITE ORDER ALGEBRAS

This paper presents the two basic problems related to symbolic representations of finite dimensio... more This paper presents the two basic problems related to symbolic representations of finite dimensional R -linear spaces endowed with an endomorphism on finite order R -algebras. In particular, the symbolic representations of either continual signals that are solutions to linear differential equations or discrete signals representing solutions to difference equations, are obtained. The symbolic representation introduced in this paper allows an unitary handling of the responses of both continual and discrete dynamical linear systems and generalises the classical frequency methods.

Research paper thumbnail of ON THE n-ORDER ACCELERATIONS DISTRIBUTION DURING RIGID MOTION

The properties of the n-order accelerations distribution of a rigid body under general motion are... more The properties of the n-order accelerations distribution of a rigid body under general motion are systematically studied based on tensor algebra. A tensor represents an R -linear mapping of the R -linear space of free vectors V into V . It may be represented by a matrix only after a basis in V was selected. Preferring an orthonormal basis simplifies the calculus, but this particular choice may conceal some essential properties. This paper uses the notion of rigid basis associated to a spherical rigid motion in order to point out some properties of the n-order accelerations tensor.

Research paper thumbnail of Computation of angular velocity and acceleration tensors by direct measurements

Acta Mechanica, 2002

The present paper investigates the properties of the angular velocity tensor ϕ and the angular ac... more The present paper investigates the properties of the angular velocity tensor ϕ and the angular acceleration tensor Ψ for rigid body motion. Three vectorial invariants of rigid body kinematics are presented. In case of tensor Ψ being non-singular, its inverse Ψ−1 is inferred. A novel procedure for automatic computation of tensor ϕ and Ψ based on measured velocity and acceleration data is developed. Depending of the type of available data, three algorithms are suggested. Numerical examples show the application of the method.

Research paper thumbnail of Algebraic computation of the twist of a rigid body through direct measurements

Computer Methods in Applied Mechanics and Engineering, 2001

The aim of the paper is to present a procedure for the automatic computation of the twist of a ri... more The aim of the paper is to present a procedure for the automatic computation of the twist of a rigid body and of its derivative with respect to time. This procedure is done through direct measurements, based on the velocities and accelerations of three non-collinear points of the rigid body. Firstly, the case of a rigid body in spherical motion is considered. Next, the case of the general motion is studied. Two algorithms for the algebraic computation of the twist of a rigid body and its derivative are further presented. Finally, an example is delivered.

Research paper thumbnail of Componentwise Stabilization of Interval Systems

Proceedings of the 17th IFAC World Congress, 2008, 2008

The componentwise stability of a linear system is a special type of asymptotic stability induced ... more The componentwise stability of a linear system is a special type of asymptotic stability induced by the existence of exponentially decreasing rectangular sets that are invariant with respect to the free response. An interval system ( )

Research paper thumbnail of Diagonally-invariant exponential stability

Proceedings of the 16th IFAC World Congress, 2005, 2005

... system (1). ∎ 3. DIESP AND MATRIX MEASURES Given a square matrix Q, consider its measure || |... more ... system (1). ∎ 3. DIESP AND MATRIX MEASURES Given a square matrix Q, consider its measure || || 0 ( ) lim(|| || 1)/ D p D p Q I Q θ µ θ θ ↓ = + − (8) associated with the matrix norm p D p QD D Q || || | 1 − = . Using the material ...

Research paper thumbnail of Qualitative Analysis Results for Arbitrarily Switching Positive Systems

Proceedings of the 18th IFAC World Congress, 2011

Research paper thumbnail of Symbolic Representation of Continual and Discrete Signals on Finite Order Algebras

This paper presents the two basic problems related to symbolic representations of finite dimensio... more This paper presents the two basic problems related to symbolic representations of finite dimensional R -linear spaces endowed with an endomorphism on finite order R -algebras. In particular, the symbolic representations of either continual signals that are solutions to linear differential equations or discrete signals representing solutions to difference equations, are obtained. The symbolic representation introduced in this paper allows an unitary handling of the responses of both continual and discrete dynamical linear systems and generalises the classical frequency methods.

Research paper thumbnail of New Results in the State-Space Analysis of Positive Linear Systems

Research paper thumbnail of Majorant Matrices in the Qualitative Analysis of Interval Dynamical Systems

Research paper thumbnail of Lyapunov functions and Lyapunov inequalities defined by Hölder p-norms for linear time-variant systems

Research paper thumbnail of Flow-Invariant Sets with Respect to the Markings of Timed Continuous Petri Nets

Proceedings of the 44th IEEE Conference on Decision and Control, 2005

The paper investigates the existence of flowinvariant sets with respect to the marking of a timed... more The paper investigates the existence of flowinvariant sets with respect to the marking of a timed continuous Petri net (TCPN) with infinite server semantics. Such a set has the property that for any initial marking belonging to the set, the marking at any moment in the evolution of the net also belongs to the set. Thus, the traditional concept of marking invariance used in PN theory, which refers to a set of places, is complemented in the sharper sense of the individual monitoring of each place. We take into consideration several types of bounded flow-invariant sets. The join-free TCPNs are treated separately from TCPNs with joins as allowing the development of supplementary investigation tools. Subsidiary to our results we give a consistent and rigorous mathematical proof for the nonnegativeness of the marking in TCPNs.

Research paper thumbnail of Matrix framework for analysis of invariant sets

International Symposium on Signals, Circuits and Systems, 2005. ISSCS 2005., 2005

For a large class of nonlinear dynamical systems, we provide results that allow testing the exist... more For a large class of nonlinear dynamical systems, we provide results that allow testing the existence of invariant sets with respect to the state space trajectories. These sets are considered as depending on time, in order to ensure the generality of the approach. The results operate as sufficient conditions formulated in terms of matrix measures associated with induced matrix norms.

Research paper thumbnail of On a conjecture in stability analysis of polytopic systems — Mimicking spectral radius properties from real to complex matrices

2014 18th International Conference on System Theory, Control and Computing (ICSTCC), 2014