A new parametrization for static output feedback control of LPV discrete-time systems

Abstract

This paper deals with the problem of synthesizing static output feedback controllers for linear parameter-varying discrete-time systems with guaranteed ℓ2 gain performance. The proposed method relies on augmenting the matrices related to the control input with a block of zeros and also augmenting the control gain accordingly with some real matrix. In this way, the closed-loop system remains the same, but extra degrees of freedom can be exploited in the proposed synthesis conditions. These conditions are described in terms of optimization problems having Linear Matrix Inequalities as constraints. Unlike other methods in the literature, all system matrices can depend on the scheduling parameter and, furthermore, the proposed approach is capable of determining a static output feedback control gain by with a one-phase one optimization problem. Numerical examples illustrate that the proposed approach is less conservative when compared to other available methods.