Robust strictly dissipative control for discrete singular systems

Abstract

The problem of strictly dissipative control for discrete singular systems with or without parameter uncertainties is focused. A necessary and sufficient condition in terms of linear matrix inequalities (LMIs) is derived guaranteeing the admissibility and strict dissipativeness of a linear discrete singular system. Then, the existence condition of a state feedback strictly dissipative controller is given by using matrix inequalities (MIs). As for an uncertain discrete singular system, the uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A sufficient condition is obtained such that the uncertain system is generalised quadratically stable and strictly dissipative. Moreover, a state feedback robust strictly dissipative controller is also constructed by using the solution of MIs.