Robust guaranteed cost control for singular Markovian jump systems with time-varying delay

Wang, Yueying; Wang, Quanbao; Zhou, Pingfang; Duan, Dengping

doi:10.1016/j.isatra.2012.04.005

Cited by 33 publications

(22 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us consider the bounded feedback control (10). Let us consider the bounded feedback control (10).…”

Section: Resultsmentioning

confidence: 99%

“…Remark 3.1. Moreover, in the papers [9,10,19,22], additional unknowns and free-weighting matrices are introduced to make the flexibility for solving LMIs. Since is not included in (8), we can first find the solutions P, S i , X i from LMI (8) and then determine from (9).…”

Section: Applying Proposition 22 For Estimation Of the Integralsmentioning

confidence: 99%

“…The finite-time stability (FTS) introduced in [6] means that the state of a system does not exceed some bound during a fixed interval time. Based on linear matrix inequality techniques, some results have been obtained for FTS and GCC for a class of linear time-delay systems, for instance [7][8][9][10]. Based on linear matrix inequality techniques, some results have been obtained for FTS and GCC for a class of linear time-delay systems, for instance [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Finite‐Time Control for Linear Time‐Varying Delay Systems With Bounded Control

Niamsup

Phát

2016

Asian Journal of Control

View full text Add to dashboard Cite

This paper develops a novel finite-time control design for linear systems subject to time-varying delay and bounded control. Based on the Lyapunov-like functional method and using a result on bounding estimation of integral inequality, we provide some sufficient conditions for designing state feedback controllers that guarantee the robust finite-time stabilization with guaranteed cost control. The conditions are obtained in terms of linear matrix inequalities (LMIs), which can be determined by utilizing the Matlab LMI Control Toolbox. A numerical example is given to show the effectiveness of the proposed method.whereM 12,12 = −0.5I, M 10,10 = − 1 1 + 27r 2 b 4 I, M 44 = −8S 3 + Q 2 , M 11,11 = − 1 , M 88 = M 99 = −12S 3 , M 12 = −2X 1 , M 13 = −2X 2 , M 14 = PD, M 16 = 6X 1 , M 45 = D T S 4 , M 1i = 0, i = 8, 9, 12, M 1,10 = P, M 1,11 = PB, M 15 = A ⊤ S 4 , M 24 = −2S 3 , M 26 = 6X 1 , M 28 = 6S 3 , M 2i = 0, i = 3, 5, 7, 9, 10, 11, 12, M 34 = −2S 3 , M 39 = 6S 3 , M 3i = 0, i = 5, 6, 8, 10, 11, 12, M 4i = 0, i = 6, 7, 10, 11, 12, M 48 = M 49 = 6S 3 , M 5i = 0, i = 6, 7, 8, 9, 10, 11, M 5,12 = S 4 ,

show abstract

“…Let us consider the bounded feedback control (10). Let us consider the bounded feedback control (10).…”

Section: Resultsmentioning

confidence: 99%

Section: Applying Proposition 22 For Estimation Of the Integralsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Finite‐Time Control for Linear Time‐Varying Delay Systems With Bounded Control

Niamsup

Phát

2016

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…Because time-delay exists widely in dynamic systems and often results in poor performance and even leads to system instability seriously. On the basis of Lyapunov-Krasovskii stability theorem [2,3], vast numbers of delay-dependent stability results for time-delay systems have been reported (see [4][5][6]). For example, the delay-range-dependent exponential stability with H ∞ performance for singular MJSs was proposed in [6].…”

Section: Introductionmentioning

confidence: 99%

“…On the basis of Lyapunov-Krasovskii stability theorem [2,3], vast numbers of delay-dependent stability results for time-delay systems have been reported (see [4][5][6]). For example, the delay-range-dependent exponential stability with H ∞ performance for singular MJSs was proposed in [6]. In order to obtain better results, various methods have been proposed in recent years, for instance Jensen's inequality, free-weighting matrix method, reciprocally convex approach and Wirtinger's inequality are applied to estimate the upper bound of cross terms in the derivative of Lyapunov-Krasovskii functions (LKF), the corresponding results were proposed in references [2,[7][8][9] respectively.…”

Section: Introductionmentioning

confidence: 99%

Improved delay-range-dependent stability criterion for Markovian jump systems with interval time-varying delay

Zhang

et al. 2015

The 27th Chinese Control and Decision Conference (2015 CCDC)

View full text Add to dashboard Cite

The delay-range-dependent stability problem for Markovian jump systems (MJSs) with interval time-varying is studied in this paper. On the basis of Lyapunov-Krasovskii stability theorem, the variables with the less conservative constraint conditions are used in Lyapunov-Krasovskii functions (LKF) to ensure the positiveness of the LKF. As a result, some sufficient conditions for stochastic stability are proposed. Finally, two examples are provided to illustrate the merits of the proposed method.

show abstract

Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

Zhang

Yan

2013

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

SUMMARYThis paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional-derivative control strategy is presented, where the derivative gain is to make the closed-loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods. Copyright

show abstract

Robust guaranteed cost control for singular Markovian jump systems with time-varying delay

Cited by 33 publications

References 18 publications

Robust Finite‐Time Control for Linear Time‐Varying Delay Systems With Bounded Control

Robust Finite‐Time Control for Linear Time‐Varying Delay Systems With Bounded Control

Improved delay-range-dependent stability criterion for Markovian jump systems with interval time-varying delay

Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

Contact Info

Product

Resources

About