High-gain output-feedback control for nonlinear systems based on multiple time scaling

We consider a general high-gain scaling technique for global control of strict-feedback-like systems. Unlike previous results, the scaling utilizes arbitrary powers (instead of requiring successive powers) of the high-gain parameter with the powers chosen to satisfy certain inequalities depending on system nonlinearities. The scaling induces a weak-cascading upper diagonal dominance (w-CUDD) structure on the dynamics. The analysis is based on our recent results on the w-CUDD property and uniform solvability of coupled state-dependent Lyapunov inequalities. The application of the general scaling technique to the design of a high-gain observer enables relaxation of the assumption in our earlier papers on cascading dominance of upper diagonal terms. The high-gain observer is coupled with a backstepping-based controller to obtain robust global stabilization in the presence of uncertainties that are incrementally linearly bounded in unmeasured states.