Robust output regulation of variable structure systems with multivalued controls

Miranda, Félix A.; Castaños, Fernando

doi:10.1109/vss.2014.6881118

Cited by 3 publications

(1 citation statement)

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“…Then the closed-loop system (13b)- (22) is well-posed and by Theorem 2 below the sliding mode is reached in finite time. The study of this kind of controllers has been reported in [31,32]. Moreover, if S = S(t) is a Lipschitz continuous set-valued mapping, then the closed-loop system (13b)- (22) represents a perturbed Moreau's sweeping process [13,19].…”

Section: Set-valued Controllermentioning

confidence: 99%

Set-Valued Sliding-Mode Control of Uncertain Linear Systems: Continuous and Discrete-Time Analysis

Miranda-Villatoro¹,

Brogliato²,

Castaños³

2018

SIAM J. Control Optim.

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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.

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