An improved stabilization method for linear time-delay systems

Fridman, Emilia; Shaked, U.

doi:10.1109/tac.2002.804462

Cited by 739 publications

(493 citation statements)

References 15 publications

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“…Similarly to Fridman & Shaked (2002), where the continuous delay was considered, we obtain for the case of piecewise-continuous delay the following result:…”

Section: Stability Of the Closed-loop Systemmentioning

confidence: 78%

“…We find a solution by solving the problem for a continuous-time system with uncertain but bounded (by the maximum sampling interval) time-varying delay in the control input. We verify that the LMI sufficient conditions for stability of (Fridman & Shaked, 2002) are valid also in the case of piecewise-continuous delay and derive LMIs for the feedback gain. The conditions which we obtain are robust with respect to different samplings with the only requirement that the maximum sampling interval is not greater than h. Moreover, the feasibility of the LMIs is guaranteed for small h if the corresponding continuous-time controller stabilizes the system.…”

Section: Introductionmentioning

confidence: 83%

“…DenotingR = R −1 andZ = Q T ZQ we obtain, similarly to (Fridman and Shaked 2002), the following Lemma 2.3 The control law of (3) stabilizes (2) for all the samplings with the maximum sampling interval not greater than h and for all the system parameters that reside in the uncertainty polytope Ω, if there exist:…”

Section: Sampled-data Stabilizationmentioning

confidence: 99%

“…The stability issue in the cases of time-varying delay without any restrictions on the derivative of the delay has been treated mainly via Lyapunov-Razumikhin functions, which usually lead to conservative results (see e.g. Hale & Lunel, 1993;Cao, Sun & Cheng, 1998;Kolmanovskii & Myshkis, 2000;Niculescu, 2001).Only recently for the first time this case was treated by Lyapunov-Krasovskii technique (Fridman & Shaked, 2002). This became possible due to a new descriptor model representation of the delay system introduced by Fridman (2001).…”

Section: Introductionmentioning

confidence: 99%

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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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“…Similarly to Fridman & Shaked (2002), where the continuous delay was considered, we obtain for the case of piecewise-continuous delay the following result:…”

Section: Stability Of the Closed-loop Systemmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 83%

Section: Sampled-data Stabilizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2004

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“…Fridman and Shaked [5] were able to use the Lyapunov-Krasovskii theorem to study the stability of system (11). In [3] they studied the stability of sampled-data systems with input delays as DDEs of the form (11) where τ 1 ∈ [0, h s ).…”

Section: Anticipative Control Unitmentioning

confidence: 99%

Anticipative and Non-anticipative Controller Design for Network Control Systems

Naghshtabrizi

Hespanha

Lecture Notes in Control and Information Science

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Summary. We propose a numerical procedure to design a linear output-feedback controller for a remote linear plant in which the loop is closed through a network. The controller stabilizes the plant in the presence of delays, sampling, and packet dropouts in the (sensor) measurement and actuation channels. We consider two types of control units: anticipative and non-anticipative. In both cases the closedloop system with delays, sampling, and packet dropouts can be modeled as delay differential equations. Our method of designing the controller parameters is based on the Lyapunov-Krasovskii theorem and a linear cone complementarity algorithm. Numerical examples show that the proposed design method is significantly better than the existing ones.

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Adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay

Yang

2008

Adaptive Control & Signal

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This paper considers the problem of adaptive robust H ∞ state feedback control for linear uncertain systems with time-varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H ∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H ∞ performance of the closed-loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method.

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An improved stabilization method for linear time-delay systems

Cited by 739 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

Anticipative and Non-anticipative Controller Design for Network Control Systems

Adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay

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An improved stabilization method for linear time-delay systems

Cited by 739 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

Anticipative and Non-anticipative Controller Design for Network Control Systems

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

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Adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay