Local stability analysis of a saturating feedback system based on LPV descriptor representation

This paper considers the local stability and the quadratic performance of a feedback system with multiple saturation non-linearities. By combining the linear parameter-varying technique and the descriptor system representation, we develop a new local stability condition that is not only numerically tractable but also less conservative than the circle criterion. A sufficient condition for the quadratic performance based on this local stability condition is also derived. Numerical examples are included to show the effectiveness of the present stability condition.