A polytopic strategy for improved non-asymptotic robust control via implicit Lyapunov functions. (February 2021)

• Record Type: Journal Article
• Authors: Tapia, Alan; Efimov, Denis; Bernal, Miguel; Fridman, Leonid; Polyakov, Andrey
• Is Part Of: Nonlinear analysis. Volume 39(2021)
• Publication Date: 2021-02
• Subjects: Finite- and fixed-time convergence -- Implicit Lyapunov functions -- Homogeneity -- Polytopic systems -- Linear matrix inequalities; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100988
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper is concerned with finite- and fixed-time robust stabilization of uncertain multi-input nonlinear systems via the implicit Lyapunov function method. Instead of splitting the system into a linear nominal model and an additive perturbation which gathers nonlinearities, parametric uncertainties, and exogenous disturbances, the methodology hereby proposed preserves some nonlinear terms in the nominal system via an exact polytopic representation which leads to design conditions in the form of linear matrix inequalities. As a result, feasible solutions are found where former approaches fail; these solutions have more accurate settling-time estimates with reduced control effort. The corresponding control law includes well-known high-order sliding modes as a particular case. Numerical simulations are provided to illustrate the advantages of the proposal.