A polytopic strategy for improved non-asymptotic robust control via implicit Lyapunov functions |
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| Institution: | 1. College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, PR China;2. College of Electrical Engineering, Guangxi University, Nanning, Guangxi 530004, PR China;3. Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, PR China;1. National Autonomous University of Mexico, Department of Control Engineering and Robotics, Division of Electrical Engineering, Engineering Faculty, C.P. 04510, México D.F., Mexico;2. Sonora Institute of Technology, 5 de Febrero 818 Sur, C.P. 85000, Cd. Obregón, Sonora, Mexico;1. Department of Control Systems and Informatics, ITMO University, 49 Kronverkskiy av., 197101 Saint Petersburg, Russia;2. Non-A team, INRIA-LNE, Parc Scientifique de la Haute Borne, 40 av. Halley, 59650 Villeneuve d’Ascq, France;3. CRIStAL (UMR-CNRS 9189), Ecole Centrale de Lille, BP 48, Cité Scientifique, 59651 Villeneuve-d’Ascq, France;1. Department of Electrical and Electronic Engineering, Imperial College London, UK;2. Dept. of Information Engineering, University of Florence, Italy |
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| 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. |
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| Keywords: | Finite- and fixed-time convergence Implicit Lyapunov functions Homogeneity Polytopic systems Linear matrix inequalities |
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