Gain scheduled state feedback control of discrete-time systems with time-varying uncertainties: an LMI approach

Abstract

This paper addresses the problems of stabilization and H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control by means of state feedback parameter-dependent gains applied to discrete-time linear systems whose matrices are affected by arbitrarily time-varying parameters belonging to a polytope. The solution of the proposed design conditions, written as a finite set of linear matrix inequalities at the polytope vertices, allows to obtain a parameter-dependent gain (i.e. a gain scheduled controller) as an analytical function of the parameters. The proposed strategy is different from similar approaches in the literature, that are based on discretizations of the space of parameters to determine interpolated control gains, or that assume special structures for the time-varying parameters or even suppose that some of the system matrices are fixed and time-invariant in order to have a convex design problem. Numerical examples illustrate the efficiency of the conditions given in the paper.