Robust control for T–S fuzzy systems with probabilistic interval time varying delay

Hu, Songlin; Zhang, Yunning; Du, Zhiwei

doi:10.1016/j.nahs.2012.02.002

Cited by 11 publications

(7 citation statements)

References 36 publications

(47 reference statements)

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“…The closed-loop Roesser type discrete-time 2-D T-S fuzzy system (17) under the control of the multi-instant fuzzy statefeedback control scheme (13) is asymptotically stable if there exist appropriately dimensional matrices P kk 0 4 0; G kk 0 ðk A Kðg 3 Þ; k 0 A Kðg 4 ÞÞ and F kk 0 ðk A Kðg 1 Þ; k 0 A Kðg 2 ÞÞ, with…”

Section: Relaxed Stabilization Conditions Via the Multi-instant Fuzzymentioning

confidence: 99%

“…Multiplying left by G fg 3 ;g 4 g ðhÞ À T and right by G fg 3 ;g 4 g ðhÞ to (22), it is easy to verify that the closed-loop Roesser type discrete-time 2-D T-S fuzzy system (17) under the control of the multi-instant fuzzy state-feedback control (13) is asymptotically stable if we have the following inequality:…”

Section: Proof Consider a New Multi-instant Lyapunov Function For Thmentioning

confidence: 99%

“…Thus, if Υ ðwpqmnÞ 4 0 for all k″ A Kðg þ 1Þ hold, Γ 4 0 evidently hold. In other words, the inequality (25) holds if the LMI-based condition (18) holds, which guarantees the asymptotical stability for the closed-loop Roesser type discrete-time 2-D T-S fuzzy system (17).…”

Section: Proof Consider a New Multi-instant Lyapunov Function For Thmentioning

confidence: 99%

“…By exploiting both the single Lyapunov function and the so-called parallel distributed compensation (PDC) control law [11], quadratic stabilization conditions for T-S fuzzy control systems have been addressed in the past two decades and many extensive results have been given in terms of LMIs, e.g., [12,13]. However, those existing quadratic stabilization conditions are very conservative and thus numerous slack variable methods have been proposed for further releasing its conservatism [14][15][16][17][18][19][20][21][22][23][24][25]. As far as the problem of control synthesis of discrete-time T-S fuzzy systems is concerned, the usage of both the nonquadratic Lyapunov function and the non-PDC control law has been fully investigated and several kinds of relaxed non-quadratic stabilization conditions have been proposed in the existing literature.…”

Section: Introductionmentioning

confidence: 99%

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Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

Xie

Zhang

2015

Neurocomputing

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Section: Relaxed Stabilization Conditions Via the Multi-instant Fuzzymentioning

confidence: 99%

Section: Proof Consider a New Multi-instant Lyapunov Function For Thmentioning

confidence: 99%

Section: Proof Consider a New Multi-instant Lyapunov Function For Thmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

Xie

Zhang

2015

Neurocomputing

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“…The authors in [6] have derived the delay-independent robust H ∞ stability criteria for discrete-time T-S fuzzy systems with infinite-distributed delays. Recently, many robust fuzzy control strategies have been proposed a class of nonlinear discrete-time systems with time-varying delay and disturbance [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. These results rely on the existence CLKF for all local models, which lead to be conservative.…”

mentioning

confidence: 99%

Delay-Dependent Generalized H2 Control for Discrete-Time Fuzzy Systems with Infinite-Distributed Delays

Li¹,

Li²,

Xia³

2012

Advances in Discrete Time Systems

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time-varying delay [4-5, 7, 11, and 13]. In fact, Distributed delay occurs very often in reality and it has been drawing increasing attention. However, almost all existing works on distributed delays have focused on continuous-time systems that are described in the form of either finite or infinite integral and delay-independent. It is well known that the discrete-time system is in a better position to model digitally transmitted signals in a dynamic way than its continuous-time analogue. Generalized H 2 control is an important branch of modern control theories, it is useful for handling stochastic aspects such as measurement noise and random disturbances [10]. Therefore, it becomes desirable to study the generalized H 2 control problem for the discrete-time systems with distributed delays. The authors in [6] have derived the delay-independent robust H ∞ stability criteria for discrete-time T-S fuzzy systems with infinite-distributed delays. Recently, many robust fuzzy control strategies have been proposed a class of nonlinear discrete-time systems with time-varying delay and disturbance [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. These results rely on the existence CLKF for all local models, which lead to be conservative. It is observed, based on the PLKF, the delay-dependent generalized H 2 control problem for discrete-time T-S fuzzy systems with infinite-distributed delays has not been addressed yet and remains to be challenging.Motivated by the above concerns, this paper deals with the generalized H 2 control problem for a class of discrete time T-S fuzzy systems with infinite-distributed delays. Based on the proposed Delay-dependent PLKF(DDPLKF), the stabilization condition and controller design method are derived for discrete time T-S fuzzy systems with infinite-distributed delays. It is shown that the control laws can be obtained by solving a set of LMIs.A simulation example is presented to illustrate the effectiveness of the proposed design procedures. Notation:The superscript "T" stands for matrix transposition, R n denotes the n-dimensional Euclidean space, R n×m is the set of all n×m real matrices, I is an identity matrix, the notation P>0(P≥0) means that P is symmetric and positive(nonnegative) definite, diag{…} stands for a block diagonal matrix. Zdenotes the set of negative integers. For symmetric block matrices, the notation * is used as an ellipsis for the terms that are induced by symmetry. In addition, matrices, if not explicitly stated, are assumed to have compatible dimensions. Problem FormulationThe following discrete-time T-S fuzzy dynamic systems with infinite-distributed delays [6] can be used to represent a class of complex nonlinear time-delay systems with both local analytic linear models and fuzzy inference rules:Advances in Discrete Time Systems 54

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Robust reliable dissipative control of nonlinear networked control systems

et al. 2016

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This article focuses on the robust reliable dissipative control issue for a class of switched discrete‐time nonlinear networked control systems with external energy bounded disturbances. In particular, nonlinearities are modeled in a probabilistic way according to Bernoulli distributed white sequence with known conditional probability. A Lyapunov–Krasovskii functional is proposed based on which sufficient conditions for the existence of the reliable dissipative controller are derived in terms of linear matrix inequalities (LMIs) which ensures exponentially stability as well as (Q,S,R) dissipative performance of the resulting closed‐loop system. The explicit expression of the desired controller gains can be obtained by solving the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness and applicability of the proposed design strategy. © 2016 Wiley Periodicals, Inc. Complexity 21: 427–437, 2016

show abstract

Robust control for T–S fuzzy systems with probabilistic interval time varying delay

Cited by 11 publications

References 36 publications

Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

Delay-Dependent Generalized H2 Control for Discrete-Time Fuzzy Systems with Infinite-Distributed Delays

Robust reliable dissipative control of nonlinear networked control systems

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