Input–output finite-time stability of discrete-time systems under finite-time boundedness

Zhang, Shuai; Guo, Yang; Wang, Shicheng; Hu, Xiaoxiang; Xie, Xu

doi:10.1080/00207721.2018.1554170

Cited by 10 publications

(3 citation statements)

References 43 publications

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“…

R

denotes a given positive definite matrix.

c_{1}

c_{2}

and d denote three given positive scalars and

c_{1} \leq c_{2}

[18–20]. Definition 3 (finite‐time H 2 ‐gain) : Assume an LTV system

Σ

constituted by (1) and (2); then, H 2 ‐gain during the finite period

(][, 0, T)

is defined as

J ()(, \sum, {bold-italicE}_{0}, T) = sup_{w ()(, t), x ()(, 0)} {[\frac{(∥∥, z ()(, t)) {_{\infty}^{2}}_{, [0, T]}}{(∥∥, w ()(, t)) {_{2}^{2}}_{, [0, T]} + x^{T} (0) E_{0} bold-italicx (0)}]}^{1 / 2}

where

x ()(, 0) \in {bold-italicR}^{n}

, and

{(∥∥, w false(t false))}_{2, (][, 0, T)} + {bold-italicx}^{normalT} ()(, 0) {bold-italicE}_{0} x ()(, 0) \neq 0

x ()(, t) \in {bold-italicR}^{n}

.…”

Section: Problem Statementmentioning

confidence: 99%

“…According to FTS, if the initial state is norm bounded, the system state does not exceed the predetermined boundary within a given finite‐time interval. The finite period here is preset, and this FTS theory concerns the boundedness of the system state over a certain period [18, 19]. Therefore, the two FTS theories are independent of each other.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite‐time bounded stabilisation for linear systems with finite‐time H ₂ ‐gain constraint

Zhang

Guo

Wang

et al. 2020

IET Control Theory & Applications

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“…

R

denotes a given positive definite matrix.

c_{1}

c_{2}

and d denote three given positive scalars and

c_{1} \leq c_{2}

[18–20]. Definition 3 (finite‐time H 2 ‐gain) : Assume an LTV system

Σ

constituted by (1) and (2); then, H 2 ‐gain during the finite period

(][, 0, T)

is defined as

J ()(, \sum, {bold-italicE}_{0}, T) = sup_{w ()(, t), x ()(, 0)} {[\frac{(∥∥, z ()(, t)) {_{\infty}^{2}}_{, [0, T]}}{(∥∥, w ()(, t)) {_{2}^{2}}_{, [0, T]} + x^{T} (0) E_{0} bold-italicx (0)}]}^{1 / 2}

where

x ()(, 0) \in {bold-italicR}^{n}

, and

{(∥∥, w false(t false))}_{2, (][, 0, T)} + {bold-italicx}^{normalT} ()(, 0) {bold-italicE}_{0} x ()(, 0) \neq 0

x ()(, t) \in {bold-italicR}^{n}

.…”

Section: Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite‐time bounded stabilisation for linear systems with finite‐time H ₂ ‐gain constraint

Zhang

Guo

Wang

et al. 2020

IET Control Theory & Applications

Self Cite

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“…The sufficient conditions of FTS for linear systems have been explored [22], [23]. Recently, sufficient and necessary conditions for FTOS have been proposed for discrete-time systems [24]- [26], impulsive linear systems [4], [27], hybrid systems [28], and switched linear systems [29]- [31].…”

Section: Introductionmentioning

confidence: 99%

Finite–Time Output Stability of Impulse Switching System With Norm–Bounded State Constraint

et al. 2019

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This paper discusses the finite-time output stability (FTOS) for the impulse switching linear system (SLS) when the norm-bounded state constraint is simultaneously considered during a scheduled finite-time period. This system is a typical hybrid system whose state trajectory instantaneously jumps according to a predetermined resetting law. The sufficient conditions of both state boundedness and output stability are proposed for the SLS in finite-time period when two typical classes of input signals are involved. Based on the linear matrix inequality, the design method of a controller using state feedback is represented to ensure state boundedness and output stability concurrently for the closed-loop system, which can effectively avoid states and the output reaching large and unacceptable values at certain points in finite time. An effective solution to the controller using a linear discretization approach is also achieved. The two simulation examples verify the proposed methods.

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Finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties

Ren

Sun

2021

Nonlinear Dyn

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Input–output finite-time stability of discrete-time systems under finite-time boundedness

Cited by 10 publications

References 43 publications

Finite‐time bounded stabilisation for linear systems with finite‐time H ₂ ‐gain constraint

Finite‐time bounded stabilisation for linear systems with finite‐time H ₂ ‐gain constraint

Finite–Time Output Stability of Impulse Switching System With Norm–Bounded State Constraint

Finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties

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Input–output finite-time stability of discrete-time systems under finite-time boundedness

Cited by 10 publications

References 43 publications

Finite‐time bounded stabilisation for linear systems with finite‐time H 2 ‐gain constraint

Finite‐time bounded stabilisation for linear systems with finite‐time H 2 ‐gain constraint

Finite–Time Output Stability of Impulse Switching System With Norm–Bounded State Constraint

Finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties

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Finite‐time bounded stabilisation for linear systems with finite‐time H ₂ ‐gain constraint

Finite‐time bounded stabilisation for linear systems with finite‐time H ₂ ‐gain constraint