Input–Output Finite-Time Stability of Linear Systems: Necessary and Sufficient Conditions

Amato, Francesco; Carannante, G.; Tommasi, G. De; Pironti, A.

doi:10.1109/tac.2012.2199151

Cited by 124 publications

(65 citation statements)

References 25 publications

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“…Theorem 3 in Amato et al (2012) can be applied to guarantee robust IO-FTS of (2) based on Definition 1. It is stated as THEOREM 1 (Amato et al, 2012): Consider the system (2).…”

Section: T)q(t)y(t) < 1 ∀T ∈ For Any Admissible W(t)mentioning

confidence: 99%

“…It is stated as THEOREM 1 (Amato et al, 2012): Consider the system (2). Given U 2 ( , R(·)), Q(·), and .…”

Section: T)q(t)y(t) < 1 ∀T ∈ For Any Admissible W(t)mentioning

confidence: 99%

“…Amato, Carannante, De Tommasi, and Pironti (2012) summarized the sufficient and necessary conditions of IO-FTS for the linear systems; in particular, Theorem 3 in this work proposed a sufficient condition of stability for the linear time-varying (LTV) systems. Although it works well for the demonstrative case in Amato et al (2012), this theorem would not be valid for systems having a singular system matrix at certain time instant or intervals. Moreover, robust stability analysis of the LTV system remains to be studied due to the existence of unknown noise input or modelling uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the problems depicted above, we propose in this research a novel IO-FTS theorem focusing on the improvement of the result in Amato et al (2012). For the IO-FTS LTV uncertain system, the issue of stability robustness is discussed, in the sense that it is robustly asymptotically stable with respect to its mean if the state mean values approach the equilibrium state.…”

Section: Introductionmentioning

confidence: 99%

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Robust stability on averaging behaviour of linear time-varying uncertain systems

Hsu

Lin

2015

Systems Science & Control Engineering

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This research proposes a new type of robust stability -mean robust asymptotic stability for linear time-varying (LTV) uncertain systems and its extension in robust asymptotic stability analysis. The system will feature this kind of stability if its state mean varies towards an equilibrium point. Robust input-output finite-time stability of the LTV uncertain system over a bounded time interval is first analysed by proposing a criterion to characterize the stability condition. The possible cases of steady-state error and state oscillation are then considered and tackled. Finally, some case studies are presented to demonstrate superiority of the proposed work.

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“…Theorem 3 in Amato et al (2012) can be applied to guarantee robust IO-FTS of (2) based on Definition 1. It is stated as THEOREM 1 (Amato et al, 2012): Consider the system (2).…”

Section: T)q(t)y(t) < 1 ∀T ∈ For Any Admissible W(t)mentioning

confidence: 99%

“…It is stated as THEOREM 1 (Amato et al, 2012): Consider the system (2). Given U 2 ( , R(·)), Q(·), and .…”

Section: T)q(t)y(t) < 1 ∀T ∈ For Any Admissible W(t)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust stability on averaging behaviour of linear time-varying uncertain systems

Hsu

Lin

2015

Systems Science & Control Engineering

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“…The problem of IO-FTS of hybrid systems was solved in [1,7]. In [9], necessary and sufficient conditions for the existence of IO-FTS of linear systems for the class of L 2 input signals were given. In [20], the issues of input-output finite-time stability and stabilization of stochastic Markovian jump systems were investigated.…”

Section: Introductionmentioning

confidence: 99%

Input-Output Finite-Time Stability of Discrete-Time Impulsive Switched Linear Systems with State Delays

Huang

Xiang

Karimi

2013

Circuits Syst Signal Process

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This paper is concerned with the problem of input-output finite-time stability (IO-FTS) for discrete impulsive switched systems with state delays. Sufficient conditions are presented for the existence of IO-FTS for such systems under the cases of certain switching, arbitrary switching, and uncertain switching. All the obtained results are formulated in a set of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed results.

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Input–Output Stability

Abdallah

Amato

Ariola

et al. 2018

Wiley Encyclopedia of Electrical and Electronics Engineering

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The earliest mathematical studies of control systems focused solely on the input–output stability of systems, as described in the works of Black, Bode, and Nyquist. In fact, most of the classical control work was limited to the input–output study of single‐input–single‐output linear and mostly time‐invariant systems. With the popularity of state‐space methods, Lyapunov stability concepts became the preferred analysis and design tools for nonlinear systems until the 1980s, when researchers became interested again in the input–output behavior of systems. The relationships between the input–output and Lyapunov stability concepts were the subject of thorough investigations, culminating with the various versions of the Kalman–Yakubovich–Popov lemma. The current studies in input–output systems are highly dynamic due to the introduction of new concepts (such as input‐to‐state stability and input–output finite‐time stability), the interaction with geometric nonlinear control, and applications to robust and adaptive control. In this article, we concentrate our discussion on continuous‐time systems and survey the classical as well as the more recent results in the input–output approach. The article starts with a collection of basic definitions, followed by the general results on the basic concepts of input–output stability and results for testing input–output stability and its relationship with Lyapunov stability. Next, we discuss the stability of interconnected systems and present the small‐gain and passivity results. Related concepts such as absolute stability, dissipativity, and input‐to‐output stability and input–output finite‐time stability are then reviewed, followed by our conclusions. We have attempted to include the main references about input–output stability, striving to be current and relevant rather than all‐encompassing.

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Input–Output Finite-Time Stability of Linear Systems: Necessary and Sufficient Conditions

Cited by 124 publications

References 25 publications

Robust stability on averaging behaviour of linear time-varying uncertain systems

Robust stability on averaging behaviour of linear time-varying uncertain systems

Input-Output Finite-Time Stability of Discrete-Time Impulsive Switched Linear Systems with State Delays

Input–Output Stability

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