Steady States of Nonlinear Systems

The concept of steady state for nonlinear systems was introduced by Isidori and Byrnes to formulate the output regulation problem. It has been noted by Chen and Huang that the concept is too limited that only neutrally stable exogenous systems are considered. In this paper, a general notion of steady state for nonlinear systems is given where the exogenous system can be unstable. This general notion is defined by the observation from some typical examples in circuit theory and the geometric implications of the classical definition of Isidori and Byrnes. That is, a steady state is characterized by the controlled invariant manifold which has the attractive property. Then by known results from stability theory, some sufficient conditions for the existence of steady states are given. The newly formulated definition of steady state has a prosperous application in a lot of problems such as observer design and output regulation.