Maximum delay bounds of linear systems under delay independent truncated predictor feedback

Wei, Yusheng; Lin, Zongli

doi:10.1016/j.automatica.2017.05.003

Cited by 34 publications

(20 citation statements)

References 26 publications

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“…Theorem 1 establishes an estimated maximum delay bound of low-gain type in the sense that the low-gain feedback parameter is sufficiently small rather than on the half axis of > 0, no matter how small the value of the delay bound D is. This is the main difference from the delay-independent truncated predictor state feedback results in our previous work, 20 which states that, for any a priori selected value of , the state feedback law would asymptotically stabilize the system as long as the delay bound is sufficiently small. Such a different scenario arises because of our delay-independent state observer design, in which the dynamic of the estimated state depends on the current input signal u(t) rather than u( (t)).…”

Section: Corollarymentioning

confidence: 58%

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A delay‐independent output feedback for linear systems with time‐varying input delay

Wei

Lin

2018

Intl J Robust & Nonlinear

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It is well known that a delay-dependent or delay-independent truncated predictor feedback law stabilizes a general linear system in the presence of a certain amount of input delay. Results also exist on estimating the maximum delay bound that guarantees stability. In the face of a time-varying or unknown delay, delay-independent feedback laws are preferable over delay-dependent feedback laws as the former provide robustness to the uncertainties in the delay.In the light of few results on the construction of delay-independent output feedback laws for general linear systems with input delay, we present in this paper a delay-independent observer-based output feedback law that stabilizes the system. Our design is based on the truncated predictor feedback design. We establish an estimate of the maximum allowable delay bound through the Razumikhin-type stability analysis. An implication of the delay bound result reveals the capability of the proposed output feedback law in handling an arbitrarily large input delay in linear systems with all open-loop poles at the origin or in the open left-half plane. Compared with that of the delay-dependent output feedback laws in the literature, this same level of stabilization result is not sacrificed by the absence of the prior knowledge of the delay.

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Section: Corollarymentioning

confidence: 58%

“…In what follows, we consider a given ∈ (−2min{Re( (A + ))}, * ]. In light of (20), it follows from (17) that if ≥ 1 ,…”

Section: Delay-independent Output Feedback Designmentioning

confidence: 99%

A delay‐independent output feedback for linear systems with time‐varying input delay

Wei

Lin

2018

Intl J Robust & Nonlinear

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“…where P k ∈ (q+m)×(q+m) is a symmetric positive-definite covariance matrix, α k is a positive coefficient and β k > 0 is a scalar coefficient used to prevent a singularˆ k . The coefficient γ k is defined similar to (18) and is given as…”

Section: Extension To Multivariable Systemsmentioning

confidence: 99%

Discrete-Time Adaptive Control for Systems With Input Time-Delay and Non-Sector Bounded Nonlinear Functions

Abidi

Postlethwaite

2019

IEEE Access

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This paper presents a discrete-time adaptive control approach for nonlinear systems with input delay. The nonlinearity is assumed to be non-sector bounded, resulting in the key technical lemma being inapplicable. The main aim of this paper is to present a general implementation inspired from Kanellakopoulos and Fu, et al. for uncertain scalar and multivariable input delay systems with uncertain parameters as well as uncertain input gain. While it has been shown by Kanellakopoulos and Fu, et al. that it is possible to design adaptive control laws that compensate for the growth of the nonlinearity for single parameter scalar systems, a rigorous analysis of multiple parameter systems is not shown. In this paper, it is shown that an adaptive controller design that compensates for the growth of the nonlinearity is possible for both multiple parameter scalar and multivariable systems with input delay. Rigorous stability proofs and simulations are presented to verify the validity of the approach. INDEX TERMS Adaptive control, discrete-time systems, nonlinear control, time-delay systems.

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“…This is a state‐feedback control law, where the gains are computed using a Lyapunov equation‐based method. However, if the plant is unstable, the amount of delay that the method can handle is limited [10]. In the case of output feedback, predictor‐based rejection control is an interesting solution [11, 12].…”

Section: Introductionmentioning

confidence: 99%

Discrete‐time adaptive control of uncertain sampled‐data systems with uncertain input delay: a reduction

Abidi

Soo

Postlethwaite

2020

IET Control Theory & Applications

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This paper proposes a discrete-time adaptive control approach for uncertain single-input and single-output (SISO) linear time-invariant sampled-data systems with uncertain, constant input time delay that has a known upper-bound, without explicitly estimating the time delay. To cope with the unknown time delay a reduction approach similar to that proposed by Artstein in 1982 is used which results in a delay-free system that simplifies the control law design. In addition, the proposed control approach is capable of coping with bounded exogenous disturbances. A rigorous stability analysis shows that the proposed control approach drives the system output to a bound around the reference signal asymptotically, in the presence of an exogenous disturbance. Moreover, simulation results are shown to verify the approach.

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Maximum delay bounds of linear systems under delay independent truncated predictor feedback

Cited by 34 publications

References 26 publications

A delay‐independent output feedback for linear systems with time‐varying input delay

A delay‐independent output feedback for linear systems with time‐varying input delay

Discrete-Time Adaptive Control for Systems With Input Time-Delay and Non-Sector Bounded Nonlinear Functions

Discrete‐time adaptive control of uncertain sampled‐data systems with uncertain input delay: a reduction

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