Constrained control of switching systems: a positive invariant approach

Benzaouia, Abdellah; Santis, Elena De; Caravani, Paolo; Daraoui, Nawal

doi:10.1080/00207170701280903

Cited by 38 publications

(14 citation statements)

References 14 publications

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“…When they are linear ones, the simple linear programming algorithms can be used. When the inequalities (6) are nonlinear ones, the existing method in [9] could solve the nonlinear inequalities (6).…”

Section: Robust Stabilizing Controller Designmentioning

confidence: 99%

“…With the development of control theory, a detailed characterization of stabilizability for the linear switching systems was given in [4,5], and several necessary and sufficient conditions of stability were proposed. Then, in [6], based on the positive invariant approach, a method to design the stabilizing controller is developed by Benzaouia et al for the nominal linear switching systems with symmetrical constrained control input.…”

Section: Introductionmentioning

confidence: 99%

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Robust Stabilizing Controller Design for the Uncertain Discrete-Time Linear Switching Systems

Fan

2013

2013 Third International Conference on Instrumentation, Measurement, Computer, Communication and Control

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This paper discussed the discrete-time linear switching systems whose discrete mode transitions are caused by discrete disturbance events and have continuous state reset functions, in the presence of parameter uncertainty state and control input bounds, the problem of robust stabilizing controller design is researched, and a method of static state feedback stabilizing controller is proposed. The relation between robust stability and existence of a robust controlled invariant set is constructed, and a test condition which can achieve in finite number steps is given. Based on the robust stability condition and the notation of linear un-saturation region for control input, the proposed robust stabilizing controller can be obtained by solving of a finite number of inequalities. At last, a numerical example is given to show the validity of the method.

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Section: Robust Stabilizing Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Stabilizing Controller Design for the Uncertain Discrete-Time Linear Switching Systems

Fan

2013

2013 Third International Conference on Instrumentation, Measurement, Computer, Communication and Control

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“…This approach has already being applied to a class of hybrid systems involving jumping parameters [7]. It has also been used to design controllers for switching systems with constrained control under complete modelling taking into account reset functions at each switch and different system's dimension [4]. The second approach, however allows saturations to take effect while guaranteeing asymptotic stability (see [3,12] and references therein).…”

Section: Introductionmentioning

confidence: 98%

Stabilization of uncertain saturated discrete-time switching systems

Benzaouia

Benmessaouda

Tadeo

2009

Int. J. Control Autom. Syst.

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This paper presents sufficient conditions for the stabilization of uncertain switching discrete-time linear systems subject to actuator saturations. These conditions are obtained by using output feedback control laws and are formulated in terms of LMIs. Two different sets of LMIs are presented for the output feedback case when saturations are allowed, that differ in complexity and conservativeness. A numerical example is used to illustrate the proposed techniques.

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“…For instance, one can only act using a certain sequence to stabilize the switched system. This class has received great interest from researchers during the last decade [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%