Improved stability and stabilisation criteria for discrete time‐delay systems via a novel double summation inequality

Zhao, Tao; Liang, Weibo; Dian, Songyi; Xiao, Jian; Wei, Zhenbo

doi:10.1049/iet-cta.2017.0791

Cited by 15 publications

(12 citation statements)

References 45 publications

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“…Due to

{\overset{M}{true}}_{1} = {\overset{M}{true}}_{2} = 0

, a potential conservatism on researching feasible solutions is caused. On the other hand, zero equations [22] is used to eliminate all zero fixed elements by substituting some variables and summation terms. However, a computation burden on researching feasible solutions may be added and the dimension of derived condition is increased.…”

Section: System Description and Problem Formulationsmentioning

confidence: 99%

“…The zero elements in the off‐diagonal term of the positive definite matrix cause conservatism to reduce the admissible delay region. Two methods as zero quality [20, 21] and double summation inequality [22] were proposed to introduce some slack variables and to derive the corresponding relaxed stability conditions. Due to the slack variables, the conservatism of the stability criteria can be reduced for magnifying the delay region as large as possible.…”

Section: Introductionmentioning

confidence: 99%

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New H _∞ observer‐based control for delayed LPV stochastic system

Chang

Chen

2021

IET Control Theory & Appl

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An H∞ observer‐based control problem of delayed Linear Parameter Varying (LPV) stochastic system is addressed in this paper. In the LPV stochastic system, stochastic behaviors and external disturbance in real environment are respectively described by stochastic difference function. Furthermore, the delay effects on state and control input are considered as time‐varying case for wide application. For the control problem, a lemma dealing with the delay terms is proposed to increase some slack variables. Based on the proposed lemma and the chosen Lyapunov‐Krasovskii function, some sufficient conditions are derived to relax the conservatism of stability criterion. Besides, disturbance effect on state and estimation error is constrained via H∞ performance for improving transient response. Through using the extended projection lemma, the derived conditions are formulated as strict Linear Matrix Inequality (LMI) problem. To avoid the potential oscillation, another lemma is proposed to separately assign the performance level during solving the conditions. All feasible solutions can be directly obtained by convex optimization algorithm without using extra calculation. Therefore, an observer‐based controller is established to guarantee the asymptotical stability and H∞ performance in the mean square. Finally, some numerical simulations are provided to demonstrate the effectiveness and applicability of the proposed method.

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“…Due to

{\overset{M}{true}}_{1} = {\overset{M}{true}}_{2} = 0

Section: System Description and Problem Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New H _∞ observer‐based control for delayed LPV stochastic system

Chang

Chen

2021

IET Control Theory & Appl

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“…The first one is to construct the LKF per si and the second step is to derive sufficient conditions guaranteeing that the forward difference of an LKF is negative. Therefore, to improve stability and stabilisation conditions many augmented LKFs and LKFs with multiple summation terms have been constructed [30][31][32]. Once the LKF is chosen, the second step comes from the inequalities to be used to derive a treatable numerical optimisation problem.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, in [31], an auxiliary function based inequality has been introduced, in [38], a free-matrix-based summation inequality has been employed, and, in [39], an improvement in the method of [35] has been presented. Several strategies have been reported for stability analysis and stabilisation problems for linear time-delay systems [32,[40][41][42][43][44][45][46][47][48], uncertain linear time-delay systems [49][50][51][52], N-TS, and TS fuzzy model with time-delays [10,[53][54][55][56][57][58][59][60][61].…”

Section: Introductionmentioning

confidence: 99%

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

Peixoto

Braga²,

Palhares

2020

IET Control Theory & Appl

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This study addresses the gain-scheduled control problem for discrete-time delayed non-linear parameter-varying (NLPV) and linear parameter-varying (LPV) systems. First, by constructing the parameter-dependent Lyapunov-Krasovskii functional and employing multiple auxiliary functions, delay-dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay-dependent linear matrix inequality conditions for the static output-feedback control design and state-feedback control design for delayed NLPV are provided. Second, the results obtained for discrete-time delayed NLPV systems are modified in a simple way to deal with discrete-time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

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“…It is well known that time-delay is an important source of system instability or oscillation [20][21][22][23][24][25][26][27]. Lyapunov-Krasovskii functional (LKF) technique is an effective method to handle stability analysis and controller design of T-S fuzzy time-delay system.…”

Section: Introductionmentioning

confidence: 99%

Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

Che

Peng

Zhao

et al. 2018

Mathematical Problems in Engineering

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This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S) fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs) are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

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Improved stability and stabilisation criteria for discrete time‐delay systems via a novel double summation inequality

Cited by 15 publications

References 45 publications

New H _∞ observer‐based control for delayed LPV stochastic system

New H _∞ observer‐based control for delayed LPV stochastic system

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

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Improved stability and stabilisation criteria for discrete time‐delay systems via a novel double summation inequality

Cited by 15 publications

References 45 publications

New H ∞ observer‐based control for delayed LPV stochastic system

New H ∞ observer‐based control for delayed LPV stochastic system

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

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New H _∞ observer‐based control for delayed LPV stochastic system

New H _∞ observer‐based control for delayed LPV stochastic system