Regional Stability and Performance Analysis for a class of Nonlinear Systems

This paper studies the problem of regional stability and performance analysis for a class of nonlinear uncertain systems. Both continuous-time and discrete-time systems are considered. Our approach is based on the use of polynomial Lyapunov functions. We show how these functions can be used to reduce the conservatism in analysis. The conditions for analysis are given in terms of linear matrix inequalities to allow feasible computational implementation. These inequalities are derived by introducing auxilary nonlinear algebraic equations and applying Finsler’s lemma. It turns out that continuous-time systems and discretetime systems require sharply different techniques in order to achieve simple linear matrix inequalities. A numerical example is used to illustrate the approach and show that the proposed method can lead to less conservative results when compared with results using quadratic Lyapunov functions.