Regional Stability and Performance Analysis for a Class of Nonlinear Discrete-Time Systems

This paper 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 continuoustime 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 discretetime 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.