Guaranteed Cost Robust Control for Switch System with Sector Uncertainty

This paper focuses on the state feedback guaranteed cost robust control of discrete-time switched system with sector uncertainty. The purpose is to design a state feedback control law such that the close-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible sector uncertainty. Using Lyapunov theory, some (linear matrix inequalities) LMIs-based efficient condition on the existence of guaranteed cost control laws is derived. Lastly, a numerical example shows the validity of the proposed design approach.