Feedback stabilization of nonlinear systems by locally bounded controls
The paper considers the feedback stabilization and output regulation of a system affine in the control \(\dot x= f(x) + g(x)u\) (here \(u \in \mathbb{R}^ m\) is a vector), and output \(y = h(x)\). A Lyapunov functions approach is examined, where the existence of a Lyapunov function should imply the stabilization. This paper focuses on stabilization and regulation with locally bounded controls. Sufficient conditions are placed on the Lyapunov functions (or rather, on the interaction of this function with the control vector field), guaranteeing the boundedness, and further conditions guarantee the continuity at the origin. Enlightening comments and examples accompany the existence results.
scientific article; zbMATH DE number 683617
scientific article