Set-valued sliding-mode control of uncertain linear systems: continuous and discrete-time analysis

Felix Miranda-Villatoro 1 Bernard Brogliato 2 Fernando Castaños 1
1 CINVESTAV-IPN - Departamento de Control Automático
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In this paper we study the closed-loop dynamics of linear time-invariant systems with feedback control laws that are described by set-valued maximal monotone maps. The class of systems considered in this work is subject to both, unknown exogenous disturbances and parameter uncertainty. It is shown how the design of conventional sliding mode controllers can be achieved using maximal monotone operators (which include the set-valued signum function). Two cases are analyzed: continuous-time and discrete-time controllers. In both cases well-posedness together with stability results are presented. In discrete time we show how the implicit scheme proposed for the selection of control actions makes sense resulting in the chattering effect being almost suppressed even with uncertainty in the system.
Keywords : Lyapunov stability linear uncertain systems Differential inclusions robust control maximal monotone maps sliding-mode control discrete-time systems
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Communication dans un congrès
IFAC 2017 - The 20th World Congress of the International Federation of Automatic Control, Jul 2017, Toulouse, France. pp.1-32
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Felix Miranda-Villatoro, Bernard Brogliato, Fernando Castaños. Set-valued sliding-mode control of uncertain linear systems: continuous and discrete-time analysis. IFAC 2017 - The 20th World Congress of the International Federation of Automatic Control, Jul 2017, Toulouse, France. pp.1-32. 〈hal-01629185〉

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