Local stabilization of minimum-phase nonlinear systems
Systems & Control Letters
New results and examples in nonlinear feedback stabilization
Systems & Control Letters
On the attitude stabilization of rigid spacecraft
Automatica (Journal of IFAC)
Linear System Theory and Design
Linear System Theory and Design
Computers & Mathematics with Applications
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Local asymptotic stability of nonlinear systems with real-parametric uncertainty or disturbance is one of the important problems in control systems literature. In this paper, we investigate this problem for nonlinear systems with time-varying disturbance. We assume that the disturbance vector is generated by an exosystem, which is neutrally stable. Thus, the disturbances that we consider include both constant and periodic signals. For this class of nonlinear systems with time-varying disturbance, we derive a necessary condition for local asymptotic stability of equilibria. As corollaries of our general result, we deduce the necessary condition obtained by Byrnes and Sundarapandian [1] for nonlinear systems with constant real parametric uncertainty, and the necessary condition obtained by Brockett [2] for nonlinear autonomous systems. We illustrate our result with several examples.