Exponential mean-square stability of time-delay singular systems with Markovian switching and nonlinear perturbations

Ding, Yucai; Zhu, Hong; Zhong, Shouming; Zeng, Yong

doi:10.1016/j.amc.2012.08.067

Cited by 23 publications

(12 citation statements)

References 40 publications

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“…Remark It is noted that Jensen's inequality was employed to bound the integral term in the aforementioned works . From Table , it can be seen that our results in Corollary are less conservative than those in the works of Wu et al and Ding et al On the other hand, it is noticed that the improvement may be relatively small. Therefore, it will be necessary to search for a better stability condition in the future research.…”

Section: Numerical Examplesmentioning

confidence: 60%

“…we also assume that 22 = −0.8 and d 1 = 0.1. For different values of 11 , the maximum allowed values of d 2 obtained by Wu et al 45 and Ding et al 46 and Corollary 1 are listed in Table 1.…”

Section: Numerical Examplesmentioning

confidence: 98%

“…Example Consider the Markovian jump system in the form of with the following parameters:

\begin{matrix} alignleft \\ align-1 A_{1} & align-2 = [\begin{array}{c} - 3.4888 & 0.8057 \\ - 0.6451 & - 3.2684 \end{array}], A_{2} = [\begin{array}{c} - 2.4898 & 0.2895 \\ 1.3396 & - 0.0211 \end{array}], \\ align-1 A_{d 1} & align-2 = [\begin{array}{c} - 0.8620 & - 1.2919 \\ - 0.6841 & - 2.0729 \end{array}], A_{d 2} = [\begin{array}{c} - 2.8306 & 0.4978 \\ - 0.8436 & - 1.0115 \end{array}] . \end{matrix}

we also assume that π 22 =−0.8 and d 1 =0.1. For different values of π 11 , the maximum allowed values of d 2 obtained by Wu et al and Ding et al and Corollary are listed in Table .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In this section, three examples will be provided to demonstrate the effectiveness and advantages of the results developed in this paper. The first example is employed to illustrate that the stability conditions obtained in Corollary 1 are less conservative than those in the work of Ding et al 45,46 Example 1. Consider the Markovian jump system in the form of (33) with the following parameters 36 :…”

Section: Numerical Examplesmentioning

confidence: 99%

See 3 more Smart Citations

Event‐triggered filter design for Markovian jump delay systems with nonlinear perturbation using quantized measurement

Xia

Zheng

2019

Int J Robust Nonlinear Control

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Summary This paper deals with the problem of mixed passivity and H∞ filter design for a class of Markovian jump delay systems with nonlinear perturbation under event‐triggered scheme and quantization. Firstly, based on an integral inequality, a new sufficient condition for the stochastic stability and performance analysis of the filtering error system is proposed. Secondly, a mode‐dependent condition for the solvability of the filter design problem is given in terms of linear matrix inequalities (LMIs). The filter parameters can be derived using feasible solutions of the presented LMIs. Finally, three numerical examples are given to illustrate the effectiveness and advantages of the proposed filter design method.

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Section: Numerical Examplesmentioning

confidence: 60%

Section: Numerical Examplesmentioning

confidence: 98%

“…Example Consider the Markovian jump system in the form of with the following parameters:

\begin{matrix} alignleft \\ align-1 A_{1} & align-2 = [\begin{array}{c} - 3.4888 & 0.8057 \\ - 0.6451 & - 3.2684 \end{array}], A_{2} = [\begin{array}{c} - 2.4898 & 0.2895 \\ 1.3396 & - 0.0211 \end{array}], \\ align-1 A_{d 1} & align-2 = [\begin{array}{c} - 0.8620 & - 1.2919 \\ - 0.6841 & - 2.0729 \end{array}], A_{d 2} = [\begin{array}{c} - 2.8306 & 0.4978 \\ - 0.8436 & - 1.0115 \end{array}] . \end{matrix}

we also assume that π 22 =−0.8 and d 1 =0.1. For different values of π 11 , the maximum allowed values of d 2 obtained by Wu et al and Ding et al and Corollary are listed in Table .…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

See 2 more Smart Citations

Event‐triggered filter design for Markovian jump delay systems with nonlinear perturbation using quantized measurement

Xia

Zheng

2019

Int J Robust Nonlinear Control

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show abstract

“…Moreover, when estimating the upper bound of the derivative of Lyapunov functional, some useful terms are ignored in [18,19]. More recently, continuous singular systems with time-varying delay in a range have been extensively studied; see, for example, [20][21][22][23][24][25][26][27] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Robust Stability and Stabilization for Singular Time-Delay Systems with Linear Fractional Uncertainties: A Strict LMI Approach

Lin

Rong

2013

Mathematical Problems in Engineering

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This paper is concerned with the problems of delay-dependent robust stability and stabilization for a class of continuous singular systems with time-varying delay in range and parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. In terms of strict linear matrix inequalities (LMIs), delay-range-dependent robust stability criteria for the unforced system are presented. Moreover, a strict LMI design approach is developed such that, when the LMI is feasible, a desired state feedback stabilizing controller can be constructed, which guarantees that, for all admissible uncertainties, the closed-loop dynamics will be regular, impulse free, and robustly asymptotically stable. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.

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Exponential mean-square stability of time-delay singular systems with Markovian switching and nonlinear perturbations

Cited by 23 publications

References 40 publications

Event‐triggered filter design for Markovian jump delay systems with nonlinear perturbation using quantized measurement

Event‐triggered filter design for Markovian jump delay systems with nonlinear perturbation using quantized measurement

Robust Stability and Stabilization for Singular Time-Delay Systems with Linear Fractional Uncertainties: A Strict LMI Approach

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