Search

We introduce a new condition for the stabilizability of discrete-time Linear Parameter-Varying (LPV) systems in the form of Linear Matrix Inequalities (LMIs). A distinctive feature of the proposed condition is the ability to handle variation in both the dynamics as well as in the input matrix without resorting to dynamic augmentation or iterative procedures. We show that this new condition contains the existing poly-quadratic stabilizability result as a particular case. A numerical example illustrates the results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of robust filters for uncertain discrete-time linear systems. The uncertainty is assumed to be time-invariant belonging to a polytope. An upper bound to the H ∞ norm of the transfer-function from the system input to the filtering error is used as performance criterion. The novelty is that the resulting robust filter has order greater than the order of the system being filtered by incorporating past output measurements. The design conditions are expressed in terms of convex problems constrained by Linear Matrix Inequalities. Performance is assessed through parameter-dependent Lyapunov functions. The results generalize existing robust filtering procedures without bringing in any additional conservatism. Simple numerical examples illustrate the procedure. [ABSTRACT FROM AUTHOR]

Abstract: We address the issue of simplifying symbolic polynomials on non-commutative variables. The problem is motivated by applications in optimization and various problems in systems and control. We develop theory for polynomials which are linear in a subset of the variables and develop algorithms to produce representations which have the minimal possible number of terms. The results can handle polynomial matrices as well as block-matrix variables. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the problem of assessing the stability of linear systems with a single time-delay. Stability analysis of linear systems with time-delays is complicated by the need to locate the roots of a transcendental characteristic equation. In this paper we show that a linear system with a single time-delay is stable independent of delay if and only if a certain rational function parameterized by an integer and a positive real number has only stable roots for any finite  and any . We then show how this stability result can be further simplified by analyzing the roots of an associated polynomial parameterized by a real number in the open interval . The paper is closed by showing counterexamples where stability of the roots of the rational function when is not sufficient for stability of the associated linear system with time-delay. We also introduce a variation of an existing frequency-sweeping necessary and sufficient condition for stability independent of delay which resembles the form of a generalized Nyquist criterion. The results are illustrated by numerical examples. [Copyright &y& Elsevier]

This paper addresses the control of linear delay systems using non-rational controllers. The structure of the controller is chosen so as to copy the structure of the plant, reproducing the delays in the state and in the output. The resulting stabilization and performance design problems are entirely expressed as linear matrix inequalities. Although the design inequalities are based on delay independent stability conditions, the overall design is delay dependent, in the sense that the controller makes use of the delay parameter of the plant. This parameter is assumed to be constant yet arbitrary. Using non-rational controllers we overcome the main difficulty faced when designing rational controllers for linear delay systems, which is to incorporate in the design problem the matrix multiplier used to prove stability with respect to the delayed part of the system. We illustrate the paper with several examples and provide extensive comparisons with existent results. [Copyright &y& Elsevier]