H∞ gain scheduling for discrete-time systems with control delays and time-varying parameters: a BMI approach

In this paper, the problem of gain scheduling for time-varying systems with time delays is investigated. By using a memory at the feedback loop, a discrete gain scheduled controller which minimizes an upper bound to the ,Hscr_infin performance of the closed loop system is determined. The design conditions, expressed in terms of bilinear matrix inequalities, are obtained from the Finsler´s Lemma combined with the Lyapunov theory. The extra variables introduced by the Finsler´s Lemma represent an alternative way in the search of better system behavior. The time-varying uncertainties are modeled using polytopic domains. The controller is obtained by the solution of an optimization problem formulated only in terms of the vertices of the polytope. No grids in the parametric space are used. Numerical examples illustrate the efficiency of the proposed approach.