Global stabilization of nonlinear cascade systems
Systems & Control Letters
Global stabilizability and observability imply semi-global stabilizability by output feedback
Systems & Control Letters
A Smooth Converse Lyapunov Theorem for Robust Stability
SIAM Journal on Control and Optimization
Brief Growth rate conditions for uniform asymptotic stability of cascaded time-varying systems
Automatica (Journal of IFAC)
Stability of cascaded fuzzy systems and observers
IEEE Transactions on Fuzzy Systems
Nonsmooth stabilization of a class of nonlinear cascaded systems
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
It is well established that, for a cascade of two uniformly globally asymptotically stable (UGAS) systems, the origin remains UGAS provided that the solutions of the cascade are uniformly globally bounded. While this result has met considerable popularity in specific applications it remains restrictive since, in practice, it is often the case that the decoupled subsystems are only uniformly semiglobally practically asymptotically stable (USPAS). Recently, we established that the cascade of USPAS systems is USPAS under a local boundedness assumption and the hypothesis that one knows a Lyapunov function for the driven subsystem. The contribution of this paper is twofold: (1) we present a converse theorem for USPAS and (2) we establish USPAS of cascaded systems without the requirement of a Lyapunov function. Compared to other converse theorems in the literature, ours has the advantage of guaranteeing a specific relationship between the upper and lower bounds on the generated Lyapunov function V and of providing a time-invariant bound on the gradient of V, which is fundamental to establish theorems for cascades.