Criteria for robust stability and stabilization of uncertain linear systems with state delay

Li, Xi; Souza, Carlos E. de

doi:10.1016/s0005-1098(97)00082-4

Cited by 425 publications

(151 citation statements)

References 15 publications

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“…Li & De Souza, 1997;Niculescu, 2001). For systems with time-varying delays such conditions were obtained via Lyapunov-Krasovskii functionals in the case where the derivative of the delay is less than one (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Robust sampled-data stabilization of linear systems: an input delay approach

2004

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A new approach to robust sampled-data control is introduced. The system is modelled as a continuous-time one, where the control input has a piecewise-continuous delay. Sufficient linear matrix inequalities (LMIs) conditions for sampled-data state-feedback stabilization of such systems are derived via descriptor approach to time-delay systems. The only restriction on the sampling is that the distance between the sequel sampling times is not greater than some prechosen h > 0 for which the LMIs are feasible. For h → 0 the conditions coincide with the necessary and sufficient conditions for continuous-time state-feedback stabilization. Our approach is applied to two problems: sampled-data stabilization of systems with polytopic type uncertainties and to regional stabilization by sampled-data saturated state-feedback.

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Section: Introductionmentioning

confidence: 99%

Robust sampled-data stabilization of linear systems: an input delay approach

2004

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“…Lemma 1. [9] Let ∈ ℝ × , ∈ ℝ × and ∈ ℝ × be matrices satisfying ≤ . For any > 0, the following inequality holds.…”

Section: Definition and Preliminariesmentioning

confidence: 99%

Pareto Optimal Control for Uncertain Markov Jump Linear Stochastic Systems

Mukaidani

Ishibashi

Furuya³

2017

Proceedings of the 4th International Conference of Control, Dynamic Systems, and Robotics (CDSR'17)

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-In this paper, a Pareto optimal strategy for uncertain Markovian linear stochastic system with multiple decision makers is investigated. By applying the guaranteed cost control principle, a set of conditions, wherein the stochastic system is exponentially mean-square stable (EMSS) and has a cost bound, is obtained using the stochastic algebraic Riccati inequality (SARI). In addition, the minimization problem of the cost bound is formulated. It is shown that the necessary conditions can be derived by a set of crosscoupled stochastic Riccati equations (CCSAREs).

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“…The maximum allowable bounds of the time-delay computed from condition (60) By considering the well known existing results from [17] where hmax = 0.8571, from [18] where hmax = 0.9999, from [20,21] where hmax = 1.0, it can be concluded that the obtained result hmax = 1.1081 of the proposed Theorem 2 is comparable with and even better than the existing results of [17−21]. Note that, in Theorem 2, the recently highly improved methods with augmented Lyapunov-Krasovskii functionals such as Park inequality [19] , Xu and Lam relaxation [15] or descriptor system approach [22] are not used.…”

Section: Extension: Multivariable Time-delay Systemmentioning

confidence: 99%

On Stability Delay Bounds of Simple Input-delayed Linear and Non-linear Systems: Computational Results

Jafarov

2013

Int. J. Autom. Comput.

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This paper deals with the problem of delay size stability analysis of single input-delayed linear and nonlinear systems. Conventional reduction, reduction linked by sliding mode, and linear memoryless control approaches are used for simple input-delayed systems to obtain the stability conditions. Several first order examples are investigated systematically to demonstrate the capabilities and limitations of the advanced stability analysis techniques including Lyapunov-Krasovskii functionals, Newton-Leibniz formula, and a newly addressed Lagrange mean value theorem. Numerical comparative results show the usefulness and effectiveness of the advanced delay size analysis techniques proposed in this paper.

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Criteria for robust stability and stabilization of uncertain linear systems with state delay

Cited by 425 publications

References 15 publications

Robust sampled-data stabilization of linear systems: an input delay approach

Robust sampled-data stabilization of linear systems: an input delay approach

Pareto Optimal Control for Uncertain Markov Jump Linear Stochastic Systems

On Stability Delay Bounds of Simple Input-delayed Linear and Non-linear Systems: Computational Results

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