New Stability Conditions for Nonlinear Systems Described by Multiple Model Approach

Abstract

This paper studies the global asymptotic stability and the tracking control problem of an uncertain non stationary continuous system described by the multiple model approach. It is based on the construction of a basis of models containing four extreme models and possibility of addition of an average model. Once the basis of models is generated, an operation of fusion of these different models is made to the level of the elementary control law and the partial output using the geometric method. New sufficient conditions for the stability are derived via Lyapunov technique. The matrices of feedback gains and tracking gains are determined while solving systems of LMI constraints (Linear Matrix Inequalities). The case of an unstable continuous nonlinear model of electrical circuit operating in pseudo-periodic system is considered to illustrate the proposed approach.