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.
- Dynamic Systems and Control Division
Nonlinear Robust H∞ Control With State-Dependent Scaling
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Hays, S, & Wu, F. "Nonlinear Robust H∞ Control With State-Dependent Scaling." Proceedings of the ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1. Arlington, Virginia, USA. October 31–November 2, 2011. pp. 581-588. ASME. https://doi.org/10.1115/DSCC2011-5994
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