Regional stability and performance analysis for a class of nonlinear discrete-time systems

Deals with the problem of regional stability and performance analysis for a class of nonlinear discrete-time systems with uncertain parameters. We use polynomial Lyapunov functions to derive stability conditions and performance criteria in terms of linear matrix inequalities (LMIs). Although the use of polynomial Lyapunov functions is common for continuous-time systems as a way to reduce the conservatism in analysis, we point out that direct generalization of such an approach to discrete-time systems leads to intractable solutions because it results in a large number of LMIs. We introduce a novel approach to reduce the computational complexity by generalizing a result of Oliveira et al. on robust stability analysis for discrete-time systems with parameter uncertainties. We point out that the proposed method can lead to less conservative results when compared with results using quadratic Lyapunov functions.