Delay-dependent stability and H ∞ control: Constant and time-varying delays

Fridman, Emilia; Shaked, U.

doi:10.1080/0020717021000049151

Cited by 664 publications

(427 citation statements)

References 26 publications

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“…Hence, the state feedback control schemes in [7] cannot be applied to design the f H control of system. Obviously, the design scheme derived in this paper is more efficient and flexible.…”

Section: Examplementioning

confidence: 99%

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RobustH_∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

et al. 2016

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Abstract. In this paper, the robust In this paper, the robust f H control problem of output dynamic observerbased control for a class of uncertain neutral systems with discrete and distributed time delays is considered. Linear matrix inequality (LMI) optimization approach is used to design the new f H output dynamic controls.The minimal f H -norm bound and the maximal perturbed bound are given. Based on the result of this paper, the constraint of matrix equality is not necessary for designing the f H observer-based controls. Finally, a numerical example is given to illustrate the efficiency of the proposed approach.

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“…Hence, the state feedback control schemes in [7] cannot be applied to design the f H control of system. Obviously, the design scheme derived in this paper is more efficient and flexible.…”

Section: Examplementioning

confidence: 99%

“…The state feedback f H controls for uncertain neutral timedelay systems had been considered in [6][7]. The output f H filtering design for neutral system without uncertainties had been proposed in [8].…”

Section: Introductionmentioning

confidence: 99%

RobustH_∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

et al. 2016

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“…Applying the hypotheses of Lemma 1 and the Schur complement [17] to (7) yields V , 0 from (19). The Lyapunov -Krasovskii functional theorem (Proposition 5.2 in Bernussou et al [18]) then implies that the systems (5) and (6) [7].…”

mentioning

confidence: 90%

“…A Remark 4: Most of the existing delay-derivative-dependent conditions [7,13,17] for the stability of systems with timevarying delay generally require a constraint of d , 1. Instead, we consider all d [ R and obtain stability for d !…”

mentioning

confidence: 99%

Improvement on robust control of uncertain systems with time-varying input delays

Wang

Goldsmith

Tan³

2007

IET Control Theory Appl.

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The problem of robust control is considered for uncertain systems with time-varying input delays. A new Lyapunov -Krasovskii functional is used together with a neutral transformation to design a robust controller for larger bounds on plant uncertainties than permitted by a recently published method. Numerical examples verify the analysis results. IntroductionRecently, the stability of uncertain systems with control input delay was investigated in Cheres et al. . The drawback is that the exact value of the time delay must be known. For time-varying delays, Lyapunov-Krasovskii functionals have been applied [9 -14]. However, the choice of Lyapunov -Krasovskii functional yields different bounds on the time delay for stability [15]. For systems with timevarying input delays, a delayed feedback control design method was proposed using the Lyapunov -Krasovskii functional approach and a neutral transformation, which gave a conservative bound on the allowable time delay [7]. One method to reduce conservativeness is to construct the Lyapunov -Krasovskii functional with a better distribution of the time delays [16].In this paper, the problem of robust control for linear systems with input delays is studied. A general method is proposed that combines a novel Lyapunov -Kranovoskii functional and a neutral transformation to obtain sufficient conditions for closed-loop robustness. These conditions are then transformed into an LMI problem to solve for the robust controller.The advantages of the new Lyapunov -Kranovoskii functional are explained and demonstrated on examples. The method allows time delays that can change at any rate and allows larger bounds on plant uncertainties than are achieved by the method of Yue and Han [7].Notation: Throughout this paper, the superscripts '21' and 'T' stand for the inverse and transpose of a matrix, respectively, R n denotes an n-dimensional Euclidean space, R mÂn is the set of all m Â n real matrices, P . 0 means that the matrix P is positive definite, I is an appropriately dimensioned identity matrix, and the symmetric terms in a symmetric matrix are denoted by Ã, for example Problem statementConsider the following uncertain system with a timevarying delay

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“…In recent developments, H ∞ related control methods have been widely investigated to overcome the input disturbance [30,31]. Based on the H ∞ performance theory, some studies are proposed in the case of external disturbance to design a suitable controller [32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Robust H _∞ state-feedback control for linear systems

2017

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This paper investigates the problem of robust H ∞ control for linear systems. First, the statefeedback closed-loop control algorithm is designed. Second, by employing the geometric progression theory, a modified augmented Lyapunov-Krasovskii functional (LKF) with the geometric integral interval is established. Then, parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill. This technique can eliminate the unnecessary enlargement of the LKF derivative estimation, which gives less conservatism. In addition, the designed controller can ensure that the linear systems are globally asymptotically stable with a guaranteed H ∞ performance in the presence of a disturbance input and parameter uncertainties. A liquid monopropellant rocket motor with a pressure feeding system is evaluated in a simulation example. It shows that this proposed state-feedback control approach achieves the expected results for linear systems in the sense of the prescribed H ∞ performance.

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Delay-dependent stability and H ∞ control: Constant and time-varying delays

Cited by 664 publications

References 26 publications

RobustH_∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

RobustH_∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

Improvement on robust control of uncertain systems with time-varying input delays

Robust H _∞ state-feedback control for linear systems

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Delay-dependent stability and H ∞ control: Constant and time-varying delays

Cited by 664 publications

References 26 publications

RobustH∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

RobustH∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

Improvement on robust control of uncertain systems with time-varying input delays

Robust H ∞ state-feedback control for linear systems

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RobustH_∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

RobustH_∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

Robust H _∞ state-feedback control for linear systems