Local Stability Analysis of Saturating Systems via Redundant LPV Descriptor Representation

Abstract

This paper considers local stability analysis of the systems with input saturation based on the LPV (linear parameter varying) descriptor representation which enables us to treat a wider class of systems and were originally proposed by Takaba. First, using the ordinary quadratic Lyapunov functions, we derive a less conservative stability condition compared to the former one by adding a new descriptor variable which is related to constancy of saturated inputs. Moreover, it is shown that this method can be easily extended to the case where piecewise quadratic Lyapunov functions are adopted. Finally we demonstrate its effectiveness through numerical examples.