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The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities , and to review some problems that remain open. An important… (More)
In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form , , and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is… (More)
In this note we consider the stability properties of a system class that arises in the control design problem of switched linear systems. The control design we are studying is based on a classical pole-placement approach.We analyse the stability of the resulting switched systemanddevelop analytic conditionswhich reduce the complexity of the stability… (More)
In this note we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A−gh , and where one of the matrices is singular. We then apply this result in a study of a feedback system with a… (More)
In this paper we consider the asymptotic stability of a class of discrete-time switching linear systems, where each of the constituent subsystems is Schur stable. We first present an example to motivate our study, which illustrates that the bilinear transform does not preserve the stability of a class of switched linear systems. Consequently, continuous… (More)
Necessary and sufficient conditions for positive realness of general transfer function matrices are derived. These conditions can be checked using eigenvalue solvers for both proper and strictly proper transfer function matrices.
This thesis deals with the stability analysis of switched linear systems. Such systems are characterised by a mixture of continuous dynamics and logic-based switching between discrete modes. This system class appears in a large variety of control systems and has a wide field of applications in the modern industrial society. While the application of switched… (More)
Necessary and sufficient conditions for strict positive realness and positive realness of general transfer function matrices are derived. The conditions are expressed in terms of eigenvalues of matrix functions of the state matrices representation of the LTI system. Illustrative numerical examples are provided.
In this paper, we consider the existence of quadratic Lyapunov functions for certain types of switched linear systems. Given a partition of the state-space, a set of matrices (linear dynamics), and a matrix-valued function A(x) constructed by associating these matrices with regions of the state-space in a manner governed by the partition, we ask whether… (More)