Parameter-memorized Lyapunov functions for discrete-time systems with time-varying parametric uncertainties

In this paper, a novel parameter-memorized Lyapunov function is proposed for stability analysis of discrete-time linear systems with time-varying parametric uncertainties. The parameter-memorized Lyapunov function depends on the uncertain parameters with a memory of a certain interval. It is shown that the previous parameter-dependent Lyapunov function is a special memoryless case of the parameter-memorized Lyapunov function, and as a result, the parameter-memorized Lyapunov function approach leads to less conservative results. Furthermore, if the length of the interval for parameter memory is sufficiently long, a nonconservative stability analysis result can be achieved. Numerical examples are provided to evaluate the obtained theoretical results.