Linear Matrices Inequalities Research Articles

Analysis and control of a class of uncertain linear periodic discrete-time systems

Feedback control problems for linear periodic systems (LPSs) with intervaltype parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality (LMI) for the asymptotical stability and state feedback stabilization, respectively, are given. Problems of $$ \mathcal{L}_2 $$ -gain analysis and control synthesis are studied. For the $$ \mathcal{L}_2 $$ -gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an $$ \mathcal{L}_2 $$ -gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an $$ \mathcal{L}_2 $$ -gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.

H2 and H∞ Filtering Design Subject to Implementation Uncertainty

This paper presents new filtering design procedures for discrete-time linear systems. It provides a solution to the problem of linear filtering design assuming that the filter is subject to parametric uncertainty. The problem is relevant, for instance, in the context of filtering implementation in real world digital devices with finite precision. The transfer function and the state space realization of the filter are simultaneously computed. Robust performance is measured by the H2 and H∞ norms of the transfer function from the noisy input to the filtering error. The results are based on the determination of an upper bound to the performance objectives. All optimization problems are linear with constraint sets given in the form of LMI (Linear Matrices Inequalities). Optimal global solutions to these problems can be readily computed. A numerical example illustrate the theory.

Constrained quadratic state feedback control of discrete-time Markovian jump linear systems

In this paper we consider the quadratic optimal control problem of a discrete-time Markovian jump linear system, subject to constraints on the state and control variables. It is desired to find a state feedback controller, which may also depend on the jump variable, that minimizes a quadratic cost and satisfies some upper bounds on the norms of some random variables, related to the state and control variables of the system. The transition probability of the Markov chain and initial condition of the system may belong to appropriate convex sets. We obtain an approximation for the optimal solution of this problem in terms of linear matrices inequalities, so that convex programming can be used for numerical calculations. Examples are presented to illustrate the usefulness of the developed results.