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Global uniform asymptotic stability of cascade time-varying nonlinear systems: case study

Concerns the global stabilization of a class of cascaded nonlinear systems. If driven subsystem (1) has a globally stable equilibrium point at x=0 when y/spl equiv/0, then the problem reduces to design an output feedback control law for the driving subsystem (2) without destabilizing (1). Previous stability results are reviewed, and the author considers a wider class of time-varying nonlinear cascaded systems and shows that the system is globally uniformly asymptotically stable (GUAS) if the zero dynamics of the first subsystem is GUAS and if the second subsystem is globally uniformly exponentially stable. The basic tools used for stability analysis are classical techniques of Lyapunov direct method.