Measurement feedback disturbance decoupling in discrete-time nonlinear systems

Kaldmäe, Arvo; Kotta, Ülle; Shumsky, Alexey; Zhirabok, Alexey

doi:10.1016/j.automatica.2013.06.013

Cited by 25 publications

(42 citation statements)

References 8 publications

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“…Note that the functions f and h in (1) may be non-smooth functions. The mathematical approach called the algebra of functions [8,10] will be used in this paper. We recall briefly the definitions and concepts to be used in this paper.…”

Section: The Algebra Of Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Faulty Plant Reconfiguration Based on Disturbance Decoupling Methods

Kaldmäe¹,

Kotta²,

Jiang³

et al. 2015

Asian Journal of Control

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The disturbance decoupling problem by dynamic measurement feedback (DDDPM) for discrete-time nonlinear control systems is considered in this paper. The mathematical approach known under the name "the algebra of functions" is used to derive an algorithm that finds, whenever possible, a measurement feedback which solves the DDDPM. Finally, the applicability of the DDDPM in fault tolerant control (FTC) is discussed.

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Section: The Algebra Of Functionsmentioning

confidence: 99%

“…The binary relation is not symmetric, see [8,10]. Binary relation Δ is used for definition of the operators and .…”

Section: Example 1 (Computation Of the Functions × And ⊕ )mentioning

confidence: 99%

Faulty Plant Reconfiguration Based on Disturbance Decoupling Methods

Kaldmäe¹,

Kotta²,

Jiang³

et al. 2015

Asian Journal of Control

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“…Disturbance decoupling has been studied for various other classes of dynamical systems and, because of the peculiarities arising in each context, it still attracts the interest of the research community. Indeed, disturbance decoupling has recently been considered for nonlinear systems [7], descriptor systems and systems over rings [8], time-delay systems [9,10], linear parameter varying systems [11,12], hybrid linear systems with state jumps [13,14], and switching linear systems [15,16,17,18,19,20,21,22,23,24,25,26,27]. The motivation for investigating possible solutions of the disturbance decoupling problem for more general classes of dynamical systems than linear time-invariant systems is not only the intrinsic theoretic interest of finding relaxed solvability conditions, but also the need to find powerful tools to solve more intricate problems like, for instance, model matching [28,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Disturbance Decoupling With Stability in Discrete-Time Switching Linear Systems: Arbitrary Switching

Zattoni¹

2016

Int. J. of Pure and Appl. Math.

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The problem of disturbance decoupling with stability consists in finding a compensator that renders the output of a dynamical system insensitive to undesired inputs, while assuring stability, in a suitable sense, of the compensated dynamics. Disturbance decoupling is a classic problem in control theory as well as a primary concern in control system design.This work deals with disturbance decoupling in discrete-time switching linear systems subject to arbitrary switching. Inaccessible and measurable disturbances are considered in a unified setting. Different problem formulations are investigated, with progressively more severe stability requirements: namely, the study starts from structural decoupling and ends to decoupling with input-to-state stability. Solvability conditions for the stated problems are proven. In particular, necessary conditions for stabilization of the inner and outer switching dynamics of the resolving subspace are shown. A convex procedure for the computation of the switching state feedback which simultaneously achieves disturbance decoupling and closed-loop stability is presented. The proposed methodology is illustrated through a worked out numerical example.

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mentioning

confidence: 99%

“…Disturbance decoupling, which is a main issue in control system design, was first solved for linear systems in the late sixties, within the geometric approach (see, e.g., [1,2] and the references therein). Since then, the problem has been reformulated for different classes of dynamical systems and, due to the peculiarities of each context, it still attracts a fair amount of research effort: e.g., nonlinear systems have recently been considered in [3], descriptor systems and systems over rings in [4], timedelay systems in [5], linear parameter varying systems in [6,7].Lately, disturbance decoupling has been tackled for switching linear systems, that are dynamical systems described by a set of linear time-invariant systemseach of them modeling a different mode of operationand a switching signal, designating the active mode at each time instant [8][9][10]. Indeed, when switching linear systems are involved, the problem of disturbance decoupling lends itself to a number of formulations, character-…”

mentioning

confidence: 99%

Stability issues in disturbance decoupling for switching linear systems

Zattoni

2015

2015 Proceedings of the Conference on Control and Its Applications

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Disturbance decoupling -i.e., the problem of making the output of a dynamical system insensitive to undesired inputs -is a classical problem of control theory and a main concern in control applications. Hence, it has been solved for many classes of dynamical systems, considering both structural and stability requirements. As to decoupling in linear switching systems, several definitions of stability apply. The aim of this contribution is investigating different decoupling problems with progressively more stringent stability requirements: from structural decoupling to decoupling with local input-to-state stability. A convex procedure for the computation of the switching compensator is presented, based on the fact that quadratic stability under arbitrary switching guarantees global uniform asymptotic stability and the latter implies local input-to-state stability. Measurable and inaccessible disturbances are considered in a unified setting. The work is focused on discrete-time systems, although all the results hold for continuous-time systems as well, with the obvious modifications.1 Introduction. Disturbance decoupling, which is a main issue in control system design, was first solved for linear systems in the late sixties, within the geometric approach (see, e.g., [1,2] and the references therein). Since then, the problem has been reformulated for different classes of dynamical systems and, due to the peculiarities of each context, it still attracts a fair amount of research effort: e.g., nonlinear systems have recently been considered in [3], descriptor systems and systems over rings in [4], timedelay systems in [5], linear parameter varying systems in [6,7].Lately, disturbance decoupling has been tackled for switching linear systems, that are dynamical systems described by a set of linear time-invariant systemseach of them modeling a different mode of operationand a switching signal, designating the active mode at each time instant [8][9][10]. Indeed, when switching linear systems are involved, the problem of disturbance decoupling lends itself to a number of formulations, character-

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Measurement feedback disturbance decoupling in discrete-time nonlinear systems

Cited by 25 publications

References 8 publications

Faulty Plant Reconfiguration Based on Disturbance Decoupling Methods

Faulty Plant Reconfiguration Based on Disturbance Decoupling Methods

Disturbance Decoupling With Stability in Discrete-Time Switching Linear Systems: Arbitrary Switching

Stability issues in disturbance decoupling for switching linear systems

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