Abstract

This paper presents a constructive method for showing stability of nonlinear systems consisting of state-dependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or when local linear models of a nonlinear system are weighted together. Stability is shown by joining multiple local quadratic Lyapunov functions properly in the state space. The stability conditions are formulated as a linear matrix inequality (LMI) problem. Hence, these can be verified efficiently by computerized methods. 1 Introduction In this paper we present a constructive method for showing stability of nonlinear systems consisting of state-dependent weighted linear systems. A large class of nonlinear systems are represented in this way, e.g. fuzzy systems [11, 12] or weighted linearized systems [5]. The second kind of systems is the result of a linearization around several states, which gives a number of linear systems. However, contrary to approaches that approxima...

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