Stability Analysis of Uncertain Discrete-time Systems with Time-varying State Delay: a Parameter-dependent Lyapunov Function Approach

This paper presents several new robust stability conditions for linear discrete-time systems with polytopic parameter uncertainties and time-varying delay in the state. These stability criteria, derived by defining parameter-dependent Lyapunov functions, are not only dependent on the maximum and minimum delay bounds, but also dependent on uncertain parameters in the sense that different Lyapunov functions are used for the entire uncertainty domain. It is established, theoretically, that these robust stability criteria for the nominal and constant-delay case encompass some existing result as their special case. The delay-dependent and parameter-dependent nature of these results guarantees the proposed robust stability criteria to be potentially less conservative.