Guaranteed cost control of linear uncertain discrete-time impulsive systems

The guaranteed cost control problem for a class of linear uncertain discrete-time impulsive systems is considered. The parametric uncertainties are assumed to be time-varying and norm-bounded. The problem is to design a robust state feedback controller such that the resulting closed-loop system is robustly exponentially stable, and the closed-loop value of a specified quadratic cost function is not more than a certain upper bound for all admissible uncertainties and for all admissible impulse time sequences. A sufficient condition for the existence of guaranteed cost state feedback controllers is derived via a time-varying Lyapunov function approach. This condition is expressed in terms of linear matrix inequalities. Furthermore, the problem of selecting a suboptimal guaranteed cost controller is formulated as a convex optimization problem. An example is provided to demonstrate the effectiveness of the proposed results.