Robust exponential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> control for uncertain time-varying delay systems with input saturation: A Markov jump model approach

Li, Bo; Shen, Hao; Song, Xiaona; Zhao, Junjie

doi:10.1016/j.amc.2014.03.088

Cited by 25 publications

(14 citation statements)

References 36 publications

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“…Definition The system of with w ( t )=0 is said to be exponentially mean‐square stable if there exist constants a >0 and b >0 such that

E (∥ x (t, φ, r (0)) ∥^{2}) < a \sup_{- \bar{τ} < t < 0} ∥ φ (t) ∥^{2} e^{- b t}

for any initial condition φ ( t )∈ R n and r (0)∈ S …”

Section: Problem Formulationmentioning

confidence: 99%

New delay‐dependent exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations

Zhang

2017

Optim Control Appl Methods

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Summary This paper deals with the problem of delay‐dependent H∞ exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations. Based on Lyapunov stability theory and linear matrix inequality method, some new H∞ exponential stability criteria are presented. The difference between this paper and other existing results is that the lower bounds of the neutral delay, the upper bounds of the neutral delay and discrete delay are considered, which will obtain some less conservative stability analysis results. Numerical examples are given to show that the proposed criteria improve the existing results.

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“…Definition The system of with w ( t )=0 is said to be exponentially mean‐square stable if there exist constants a >0 and b >0 such that

E (∥ x (t, φ, r (0)) ∥^{2}) < a \sup_{- \bar{τ} < t < 0} ∥ φ (t) ∥^{2} e^{- b t}

for any initial condition φ ( t )∈ R n and r (0)∈ S …”

Section: Problem Formulationmentioning

confidence: 99%

New delay‐dependent exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations

Zhang

2017

Optim Control Appl Methods

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“…Recently, some investigations are carried out on the MJSs with actuator saturation [37][38][39][40][41][42][43][44][45][46]. By applying appropriate Lyapunov functions, robust H ∞ controller for uncertain discrete-time MJSs is design to guarantee the stochastic stability of the corresponding closed-loop systems in [39].…”

Section: Markov Jump Systems (Mjss) Driven By Continuous-time Markov mentioning

confidence: 99%

“…Zhao et al investigated finite-time H ∞ control for a class of MjSs with actuator saturation and obtained a series of results [43][44][45]. Finite-time H ∞ control for a class of discrete-time Markov jump systems with actuator saturation was probed via dynamic anti-windup design in [46].…”

Section: Markov Jump Systems (Mjss) Driven By Continuous-time Markov mentioning

confidence: 99%

“…Compared with the existing results in [45,46,47,48], we investigate a class of Markovian jump continuous-time singular systems even with a standard Wiener process, not Markovian jump discrete-time systems. Compared with the existing results in [43,44,50], we introduce the general unknown transition rates for the Markov process, which is more general than the partly accessible transition rates. Here, the standard Wiener process, general unknown transition rates and singular system matrix are introduced to increase the difficulty of our research.…”

Section: Problem Formulationmentioning

confidence: 99%

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An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

Kao

Xie

Wang

2015

Journal of the Franklin Institute

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“…Applications may be found in many processes, such as fault-tolerant systems, biology systems, distributed network systems, robotic manipulator systems and wireless communication systems [1][2][3]. On the hypothesis of known transition probabilities, fruitful results on stability, stabilization, sliding mode control, H 2 and H ∞ control are reported in [1][2][3] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

H?Control for Markovian Jump Delay Systems with Distributed Delay

Wu¹,

Xiong²,

Shu³

2018

Proceedings of the 2017 2nd International Conference on Electrical, Control and Automation Engineering (ECAE 2017)

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Abstract-This paper aims to design the H∞ controller for continuous Markovian jump systems with distributed delay. First, a new integral inequality is proposed. Next, based on the constructed Lyapunov functional, the new introduced inequality is used to investigate the delay-dependent stability condition for the systems. Third, a delay-dependent condition is derived for the solvability of the H∞ control problem, and the desired controller can be obtained. Finally, a numerical example is provided to demonstrate the effectiveness and the less conservatism of the method.

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Robust exponential H∞ control for uncertain time-varying delay systems with input saturation: A Markov jump model approach

Cited by 25 publications

References 36 publications

New delay‐dependent exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations

New delay‐dependent exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations

An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

H?Control for Markovian Jump Delay Systems with Distributed Delay

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