Parameter-varying state feedback control for discrete-time polytopic systems

This article provides sufficient stability conditions for time-varying discrete-time polytopic systems along with H-infinity performance optimisation. First, the homogeneous polynomially parameter-dependent matrix function (HPP-DMF for abbreviation) is introduced. Then, based on the HPP-DMF, new parameter-varying state feedback controller and Lyapunov functions are designed. By applying the controller and Lyapunov functions, some new conditions, which are expressed in terms of linear matrix inequalities (LMIs) and admit more freedom in guaranteeing the stability of closed-loop systems, are obtained. In addition, it is shown that as the degree increases the conditions become less conservative. Although the number of LMIs increases, each LMI is simple and easy to be fulfilled. Furthermore, the determination of guaranteed disturbance attenuation is addressed. Finally, two examples are given to demonstrate the applicability of the proposed approach.