Semiglobal asymptotic stabilization of nonlinear systems with triangular zero dynamics by linear feedback

This paper studies the problem of semiglobal asymptotic stabilization (SGAS) by state feedback for a class of nonlinear systems beyond the normal form. The zero dynamics is of a triangular structure and assumed to satisfy minimum-phase and ISS conditions. By taking advantage of the triangular structure, we develop a semiglobal backstepping approach for the construction of a set of parameterized Lyapunov functions, associated sublevel sets and nested high-gain linear state feedback laws, step-bystep. To prevent the shrinking of domains of attraction and overcome the complexity of the semiglobal design based on the rational Lyapunov functions (Teel and Praly, 1995), we introduce the notion of sublevel set and a set of parameterized Lyapunov functions that are well-defined in the entire space, and show how they can be constructed recursively, which are instrumental in solving the SGAS problem by partial linear state feedback. (C) 2020 Elsevier Ltd. All rights reserved.