Robust guaranteed cost control for discrete-time systems with multiple delays in state

This paper deals with the problem of robust guaranteed cost control for generalized discrete time-delay systems with norm-bounded uncertainties. Based on linear matrix inequality (LMI) technique, we develop discrete Lyapunov function approach for robust performance analysis and robust stabilization via linear memoryless state feedback.\ud We show that the feasibility of a linear matrix inequality guarantees the solvability of the addressed robust guaranteed cost control problem. Moreover, we show that the robust guaranteed cost control for the generalized discrete time-delay systems with norm-bound uncertainties can be viewed as an H1 type condition for an uncertainty-free system. We also have presented an upper bound for the cost function of the underlying system with the designed controller for the case of initial state values being a zero mean random variables. An example is given to show the potential of the proposed techniques