Stabilization of 2D saturated systems by state feedback control

Hmamed, Abdelaziz; Mesquine, Fouad; Tadeo, Fernando; Benhayoun, Mohamed; Benzaouia, Abdellah

doi:10.1007/s11045-010-0107-2

Cited by 57 publications

(24 citation statements)

References 34 publications

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“…This function was introduced in [19]. Matrices P ss and F s are given by: , which are generally difficult and lead to nonlinear terms, the following assumptions are introduced, as is generally the case in the literature: …”

Section: Multiple Lyapunov Functionsmentioning

confidence: 99%

Stabilization of Two-Dimensional T–S Fuzzy Systems

Benzaouia

2014

Advanced Takagi‒Sugeno Fuzzy Systems

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In the last two decades, the two-dimensional (2D) system theory has been paid considerable attention by many researchers. The 2D linear models were introduced in the 70s [1,2] [6]). On the other hand, the stabilization problem has not been fully investigated and is not completely solved. The stability of 2D discrete linear systems can be reduced to checking the stability of 2D characteristic polynomial [7,8]. This appears to be a difficult task for the control synthesis problem. In the literature, various types of easily checkable, but only sufficient conditions for asymptotic stability and stabilization problems for 2D discrete linear systems have been proposed [9][10][11][12][13].This chapter is interested to nonlinear 2D model Roesser systems described with T-S models. The obtained fuzzy system is then a set of r linear 2D systems linked between themselves by membership functions. The objective of this work is to design stabilizing controllers for this class of systems. To the best of our knowledge, no works have been directly considered fuzzy 2D systems before, except the work of the authors [14]. To this end, common Lyapunov quadratic and multiple Lyapunov functions are used. In this context, sufficient conditions of stabilizability are presented. Furthermore, these conditions are presented in the form of a set of LMIs for the state feedback control case. The results of this chapter were initially published in [14][15][16].

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Section: Multiple Lyapunov Functionsmentioning

confidence: 99%

Stabilization of Two-Dimensional T–S Fuzzy Systems

Benzaouia

2014

Advanced Takagi‒Sugeno Fuzzy Systems

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“…The stability and stabilisation problems of 2-D discrete systems have been studied by many researchers (see Bachelier, Paszke, Yeganefar, & Mehdi, 2013;Bouagada & Dooren, 2013;Du & Xie, 1999;Du & Xie, 2002;Hinamoto, 1997;Hmamed, 1997;Li, Ho, & Chow, 2005;Paszke, Lam, Gałkowski, Xu, & Lin, 2004). Recently, some results on stability and stabilisation of 2-D continuous systems have also been obtained (see Benhayoun, Mesquine & Benzaouia, 2013;Benzaouia, Benhayoun & Tadeo, 2011;Galkowski, Paszke, Sulikowski, Rogers, & Owens, 2002;Ghamgui, Yeganefar, Bachelier, & Mehdi, 2011;Hmamed, Mesquine, Tadeo, Benhayoun, & Benzaouia, 2010).…”

Section: Introductionmentioning

confidence: 99%

H_∞control of a class of 2-D continuous switched delayed systems via state-dependent switching

Ghous

Xiang

2015

International Journal of Systems Science

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This paper addresses the problem of state feedback H ∞ stabilisation of 2-D (two-dimensional) continuous switched state delayed systems represented by the Roesser model using the multiple Lyapunov functional approach. First, an asymptotical stability condition of 2-D continuous switched systems with state-dependent switching is derived. Second, a sufficient condition for H ∞ performance of the underlying system is established. Third, a state feedback controller is proposed to ensure that the resulting closed-loop system has a prescribed H ∞ performance level under a state-dependent switching signal. All the results are developed in terms of linear matrix inequalities. Finally, three examples are provided to demonstrate the validity and effectiveness of the proposed method.

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“…In the past decade, many important methodologies and techniques have been developed for analysis and synthesis problems of 2-D systems, which include, but are not limited to, the stability and performance analysis problems [3], [5], [10], [13], [18], [25], [31], [39], [41], robust and/or H ∞ control problems [9], [21], [34], [40], [43], robust and/or H ∞ filtering problems [4], [8], [28], as well as the H ∞ model reduction problems [12]. Since time delays frequently occur in practical systems and are often the source of instability, 2-D systems with various types of delays have also been a research focus in the past few years, and a great number of results have been reported in the literature, see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…[3], [4], [31], [41]. Note that, in the context of 2-D systems, the stochastic perturbation issue has been taken into account in [13], [44] and the saturated nonlinearities have been studied in [3], [18], [33].…”

Section: Introductionmentioning

confidence: 99%

H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements

Liang

Wang

Liu

2015

Journal of the Franklin Institute

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In this paper, the H ∞ output-feedback control problem is investigated for a class of two-dimensional (2-D) nonlinear systems with time-varying delays under imperfect measurements. Randomly occurring nonlinearities (RONs) are introduced in the system to account for probabilistic nonlinear disturbances typically caused by networked environments and governed by a sequence of random variables obeying the Bernoulli distribution. The imperfect measurement outputs are subject to both data missing and randomly occurring sensor saturations (ROSSs), which are put forward to characterize the network-induced phenomena such as probabilistic communication failures and limited capacity of the communication devices. The aim of this paper is to design an output-feedback controller such that the closed-loop system is globally asymptotically stable in the mean square and the prescribed H ∞ performance index is satisfied. Sufficient conditions are presented by resorting to intensive stochastic analysis and matrix inequality techniques, which not only guarantee the existence of the desired controllers for all possible time-delays, RONs, missing measurements and ROSSs but also lead to the explicit expressions of such controllers. Finally, a numerical simulation example is given to demonstrate the applicability of the proposed control scheme.

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Stabilization of 2D saturated systems by state feedback control

Cited by 57 publications

References 34 publications

Stabilization of Two-Dimensional T–S Fuzzy Systems

Stabilization of Two-Dimensional T–S Fuzzy Systems

H_∞control of a class of 2-D continuous switched delayed systems via state-dependent switching

H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements

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Stabilization of 2D saturated systems by state feedback control

Cited by 57 publications

References 34 publications

Stabilization of Two-Dimensional T–S Fuzzy Systems

Stabilization of Two-Dimensional T–S Fuzzy Systems

H∞control of a class of 2-D continuous switched delayed systems via state-dependent switching

H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements

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H_∞control of a class of 2-D continuous switched delayed systems via state-dependent switching