State-dependent scaling for robust nonlinear control: techniques and effectiveness

This paper focuses on the state-dependent (SD) scaling technique for robust nonlinear control. In contrast with linear uncertain systems, scaling factors for small gain conditions can be functions of state variables. This paper looks at the small gain characterization with quadratic Lyapunov functions for robust nonlinear control analysis and synthesis. Then, it is demonstrated that state-dependence of scaling in the characterization has great advantage when we direct our attention to the domain of attraction in the state space, i.e., global, semi-global or regional stabilization. The SD scaling method can detect and guarantee much larger domains of attraction than the state-independent one. For controller design, the SD scaling also prevents controllers from having unnecessarily high gain. In order to find such effective scaling factors systematically, the problem of maximizing the guaranteed region is formulated and computationally effective approaches to analysis and synthesis problems are proposed.