Finite-time stability of discrete-time systems

Amato, Francesco; Carbone, Marco; Ariola, M.; Cosentino, Carlo

doi:10.23919/acc.2004.1386778

Cited by 29 publications

(15 citation statements)

References 7 publications

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“…Remark The definition of Lyapunov Asymptotical Stability (LAS) is independent of FTS. For linear systems, LAS is a structural property of the system, depending only on the system matrix, while FTS clearly depends on the kind and amplitude of the inputs acting on the system .…”

Section: Problem Formulationmentioning

confidence: 99%

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

Chen

Sun

2019

Asian Journal of Control

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This paper investigates the problem of finite time stability of linear time‐varying system with delay. By constructing an augmented time‐varying Lyapunov functional and using the Wirtinger‐type inequality deductively, delay‐dependent finite time stability conditions are derived and presented in terms of differential linear matrix inequalities (DLMIs). Then, the DLMIs are transformed into a series of recursive linear matrix inequalities (RLMIs) by discretizing the time interval into equally spaced time distances, and an algorithm is given to solve the RLMIs. Examples illustrate the feasibility and effectiveness of the proposed method.

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Section: Problem Formulationmentioning

confidence: 99%

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

Chen

Sun

2019

Asian Journal of Control

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“…For linear systems, there are necessary and sufficient FTS conditions based on differential and difference linear matrix inequalities (DLMIs) and based on the state transition matrix of the system [6]- [8]. The FTB analysis is more complex and, to the best of the authors knowledge, a FTB necessary and sufficient condition exists only for continuous time systems [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Finite time boundedness and stability analysis of discrete time uncertain systems

Kussaba

Ishihara

Borges

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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In this paper the problems of finite time boundedness and stability of uncertain systems in discrete-time are addressed. By using the Finsler lemma, novel parameter dependent linear matrix inequalities analysis conditions are designed. These conditions can be efficiently solved using a homogeneous polynomial relaxation procedure and readily available numerical solvers.In the numerical examples section, it is shown that the proposed finite time conditions are less conservative than others linear matrix inequality based conditions proposed in the literature.

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“…(Introduction) 1 B $%&'(), Lyapunov B%&$;a 9<5, 9: ,$C0&""#X &$L,Lyapunov B%&8 [\ $X [1][2][3][4][5][6] [14] (C LD $ :#"WX, C #"$5 , #"$/ ?<,/ #"$1):;6 0 , , …”

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The Analysis of Finite-time Stability for Time Varying polytopic systems

Zhong

Duan

2006

2007 Chinese Control Conference

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The problem of finite-time stability for time varying polytopic systems is concerned in this paper. Three equivalent conditions for FTS is proposed. To facilitate the systems design, a sufficient LMI criterion on the FTS is further given. For the influence of the input disturbance, we also give the definition of FTB and a sufficient LMI criterion. A numerical example is employed to illustrate the effect of the proposed approach.

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Finite-time stability of discrete-time systems

Cited by 29 publications

References 7 publications

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

Finite time boundedness and stability analysis of discrete time uncertain systems

The Analysis of Finite-time Stability for Time Varying polytopic systems

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