Abstract
This paper is concerned with the local stability and the quadratic performance of a piecewise affine system. In terms of piecewise quadratic Lyapunov functions, we derive new conditions that explicitly characterize inner approximations of the domain of attraction and the domain of quadratic performance for the piecewise affine system. Furthermore, we apply these analysis conditions to a saturating system which can be encountered in many practical control problems. It turns out for the saturating system that the present stability condition is not as conservative as the local circle criterion. We also propose two numerical methods for maximizing the inner approximation of the domain of attraction. A numerical example is included to show the effectiveness of the present results.
