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Journal Articles (Review Article) International Journal of Robust and Nonlinear Control Year : 2023

Generalized homogeneous control with integral action

Abstract

A generalized homogeneous control with integral action for a multiple-input plant operating under uncertainty conditions is designed. The stability analysis is essentially based on a special version of the non-smooth Lyapunov function theorem for differential equations with discontinuous right-hand sides. A Lyapunov function for analysis of the closed-loop system is presented. For negative homogeneity degree, this Lyapunov function becomes a strict Lyapunov function allowing an advanced analysis to be provided. In particular, the maximum control magnitude and the settling-time of the closed-loop system are estimated and a class of disturbances to be rejected by the control law is characterized. The control parameters are tuned by solving a system of Linear Matrix Inequalities (LMIs), whose feasibility is proved at least for small (close to zero) homogeneity degrees. The theoretical results are illustrated by numerical simulations.
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hal-03993724 , version 1 (17-02-2023)

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Yu Zhou, Andrey Polyakov, Gang Zheng. Generalized homogeneous control with integral action. International Journal of Robust and Nonlinear Control, 2023, ⟨10.1002/rnc.6612⟩. ⟨hal-03993724⟩
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