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This paper deals with the output feedback [H.sub.[infinity]] control design problem for continuous-time switched linear systems. More specifically, the main goal is to design a switching rule together with a dynamic full order linear controller to satisfy a prespecified [H.sub.[infinity]] level defined by the [L.sub.2] gain from the input to the output signal. Initially, the state feedback version of this problem is solved in order to put in evidence the main difficulties we have to face toward the solution of the output feedback control design problem. The results reported in this paper are based on the so called Lyapunov--Metzler inequalities, which express a sufficient condition for switched linear systems global stability. The solution of the previously mentioned output feedback control design problem through a linear matrix inequality based method is the main contribution of the present paper. An academic example borrowed from literature is used for illustration. [DOI: 10.1115/1.4001711]

This technical note addresses the discrete-time Markov jump linear systems [H.sub.[infinity]] filtering design problem. First, under the assumption that the Markov parameter is measurable, the main contribution is the linear matrix inequality (LMI) characterization of all linear filters such that the estimation error remains bounded by a given [H.sub.[infinity]] norm level, yielding the complete solution of the mode-dependent filtering design problem. Based on this result, a robust filter design able to deal with polytopic uncertainty is considered. Second, from the same LMI characterization, a design procedure for mode-independent filtering is proposed. Some examples are solved for illustration and comparisons. Index Terms--Discrete-time systems, linear matrix inequalities (LMIs), Markov jump linear systems, robust filtering.

This paper is devoted to stability analysis and control design of switched linear systems in both continuous and discrete-time domains. A particular class of matrix inequalities, the so-called Lyapunov--Metzler inequalities, provides conditions for open-loop stability analysis and closed-loop switching control using state and output feedback. Switched linear systems are analyzed in a general framework by introducing a quadratic in the state cost determined from a series of impulse perturbations. Lower bounds on the cost associated with the optimal switching control strategy are derived from the determination of a feasible solution to the Hamilton--Jacobi--Bellman inequality. An upper bound on the optimal cost associated with a closed-loop stabilizing switching strategy is provided as well. The solution of the output feedback problem is based on the construction of a full-order linear switched filter whose state variable is used by the mechanism for the determination of the switching rule. Throughout, the theoretical results are illustrated by means of academic examples. A realistic practical application related to the optimal control of semiactive suspensions in road vehicles is reported. Index Terms--Linear matrix inequalities (LMIs), output feedback control, switched systems.

In this brief, a procedure for digital filters design is presented. The main purpose is to show that a digital filter and its realization can be simultaneously determined such as to minimize an upper bound of the [H.sub.2] norm of the estimation error and impose a certain degree of robustness against practical uncertainties as for instance, finite word length implementation, roundoff errors, and numerical precision. The optimal filter and its state-space realization are jointly determined from the solution of a convex programming problem expressed in terms of linear matrix inequalities. A simple illustrative example is presented for comparison purposes making clear the advantages of the reported results. Index Terms--Digital filters, Kalman filters, optimization, robustness.

This note provides sufficient robust stability conditions for continuous time polytopic systems. They are obtained from the Frobenins--Perron Theorem applied to the time derivative of a linear parameter dependent Lyapunov function and are expressed in terms of linear matrix inequalities (LMI). They contain as special cases, various sufficient stability conditions available in the literature to date. As a natural generalization, the determination of a guaranteed [H.sub.2] cost is addressed. A new gain parametrization is introduced in order to make possible the state feedback robust control synthesis using parameter dependent Lyapunov functions through linear matrix inequalities. Numerical examples are included for illustration. Index Terms--Linear matrix inequalities (LMIs), linear systems, robust control design, robust stability and performance.

A procedure is proposed for reduced-order filtering design using both [H.sub.2] and [H.sub.infinity] norms, based on the solution of a convex programming problem expressed in terms of lean matrix inequalities (LMI). The proposed method is verified by means of illustrative examples, and is found to have a smaller computational burden and a better performance than other available methods.