Stability Analysis for A Class of Parameter Dependent Piecewise Affine Systems

This work builds on the stability analysis of a class of piecewise affine systems reported in [1]. This class of hybrid systems models parameter dependent nonlinear systems in the form of parameter dependent piecewise affine systems in which the matrices and vectors defining piecewise affine system are affine functions of parameters. The proposed stability analysis technique relies on formulating the search for a piecewise quadratic Lyapunov function as a Bilinear Matrix Inequality. This can be solved iteratively as a set of two optimization problems involving linear matrix inequalities which can be solved numerically very efficiently. The implementation of the proposed method is illustrated by an example.