Design of H∞ static output feedback control for discrete‐time systems with limited actuator

Abstract

AbstractIn this paper, static output feedback (SOF) control analysis and synthesis are conducted for linear discrete‐time systems subject to actuator saturation with an H∞ setting. Typically, the SOF problem is nonconvex; the existence of static output feedback control can be expressed in terms of the solvability of bilinear matrix inequalities (BMIs). Because these BMIs are difficult to solve, they are usually solved by transforming the BMI problem into an iterative linear matrix inequality (ILMI) problem. The actuator saturation problem is also considered since the driving capacity of an actuator is limited in practical applications. Using the classical approach, singular value decomposition (SVD), the H∞ SOF controller design problem for systems with actuator saturation can be expressed in terms of an eigenvalue problem (EVP). The coordination between the minimization of the attenuation level of the H∞ performance and the maximization of the estimation of the region of attraction are considered in our approach in the solution of the proposed EVP. Finally, some numerical examples are given to describe the proposed design procedure.