Performance analysis of saturated systems via two forms of differential inclusions

In this paper we develop a systematic Lyapunov approach to the regional stability and performance analysis of saturated systems in a general configuration. The only assumptions we make about the system are local stability and well-posedness of the algebraic loop. Problems to be considered include the estimation of the domain of attraction, the reachable set under a class of norm-bounded disturbances and the nonlinear L2gain. The regional analysis is established upon an effective treatment of the algebraic loop and the deadzone function. This treatment yields two forms of differential inclusions, a polytopic differential inclusion (PDI) and a normbounded differential inclusion (NDI), for the description of the original system. The corresponding conditions for stability and performance are derived as Linear Matrix Inequalities (LMIs).