An L/sub 2/-gain analysis of piecewise affine systems by piecewise quadratic storage functions

Piecewise affine (PWA) systems, which belong to a class of hybrid systems receiving a lot of attention, are useful for describing dynamics of real-world systems. A PWA system, whose dynamic is composed of a finite number of affine dynamics and switching laws, is at an advantage because existing analysis and control methods for linear systems may be applied to the system with a little modification. Based on this concept, in existing literature, some analysis conditions via piecewise quadratic functions were suggested for PWA systems whose switchings of dynamics depend only on their states. The conditions, however, are not satisfactory enough, because real-world systems like control systems with input saturations and dead-zone nonlinearities, which can be frequently described as PWA systems, are usually dominated by switching laws which depend both on their states and on inputs. This paper discusses the L/sub 2/-gain analysis problem via piecewise quadratic storage functions for PWA systems whose switching laws of dynamics depend not only on their states but also on exogenous inputs.