H∞ parameter-dependent state feedback control of linear time-varying systems in polytopic domains

The synthesis of H∞parameter-dependent state feedback controllers for linear time-varying systems in polytopic domains is addressed by means of linear matrix inequalities. Differently from other gain scheduled approaches in the literature, all the system matrices are supposed to be affected by time-varying parameters, which have bounded rates of variation and belong to a polytope. Moreover, there are no assumptions on the structure of the parameters and no gridding technique is required to determine the parameter-dependent controller. The scheduled state feedback gain is calculated through an analytical expression using the time-varying parameters and a set of matrices obtained from the feasibility of a linear matrix inequality problem. The proposed convex design conditions, based on parameter-dependent Lyapunov functions, allow to improve the H∞performance of the system when compared to other control strategies and also to cope with problems of time-varying actuator failures.