Nonlinear Robust H∞ Control With State-Dependent Scaling

This paper addresses the design of nonlinear robust H∞ controllers for nonlinear uncertain systems with polynomial vector field and norm bounded uncertainties. We derive state-dependent matrix inequalities, using Lyapunov’s direct method, that stabilize the nonlinear systems and guarantee robust performance using nonlinear state-feedback control. The state-dependent synthesis conditions incorporate state-dependent scaling to minimize the ℒ2 gain of the disturbance/output. Sum-of-squares (SOS) optimization is applied to solve the resulting synthesis condition with optimized ℒ2 gain for the nonlinear system, without requiring an iterative approach. Finally, a design example of nonlinear Van der Pol equation is presented.