Exponential stability of discrete time uncertain systems with time-varying delay

Hsien, Tsung-Lieh; Lee, Chien-Hua

doi:10.1016/0016-0032(95)00058-5

Cited by 14 publications

(9 citation statements)

References 9 publications

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“…Definition 1 [3] .The uncertain time-delay system(1) is said to be exponentially stable if there exist constant scalars 0 ≤ < 1 and ≥ 1 such that…”

Section: Resultsmentioning

confidence: 99%

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A new exponentially stable sliding mode control approach for a class of uncertain discrete systems with time delay

Yuan

2012

2012 24th Chinese Control and Decision Conference (CCDC)

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The exponentially stable sliding mode control problem for a class of uncertain discrete-time systems with delay is considered in this paper. A new sufficient condition is given to design the exponentially stable sliding mode surface. Based on the Lyapunov theory, a design strategy is then derived for the hitting controller. And all the conditions are expressed in terms of linear matrix inequalities. Finally, a numerical example is given to demonstrate the validity of the results.

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“…Definition 1 [3] .The uncertain time-delay system(1) is said to be exponentially stable if there exist constant scalars 0 ≤ < 1 and ≥ 1 such that…”

Section: Resultsmentioning

confidence: 99%

“…For the last decade,several works have proposed criteria for the robust stabilization of time-delay systems [1,2] . Recently, the problems of robust stability of discrete time-delay systems have been studied [3] . In [4], Kua considered the robust stability for uncertain discretetime systems by LMI approach.…”

Section: Introductionmentioning

confidence: 99%

A new exponentially stable sliding mode control approach for a class of uncertain discrete systems with time delay

Yuan

2012

2012 24th Chinese Control and Decision Conference (CCDC)

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“…The problem of stability and robustness of difference systems has been extensively studied in the last years [1][2][3][4][5][6][7]. However, mainly systems with linear leading parts were investigated.…”

Section: Introductionmentioning

confidence: 99%

New Conditions for the Exponential Stability of Pseudolinear Difference Equations in Banach Spaces

Medina

2016

Abstract and Applied Analysis

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We study the local exponential stability of evolution difference systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in infinite-dimensional Banach spaces, in the sense that the exponential stability for a given pseudolinear equation persists under sufficiently small perturbations. The main methodology is based on a combined use of new norm estimates for operator-valued functions with the “freezing” method.

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“…The resulting computational complexity is N P (cf. We know that (14) is also a sufficient condition for stability of the time-variant system (see for example [4]). Therefore, we have the following lemma:…”

Section: B the Delays Interfacementioning

confidence: 98%

“…The derived conditions for stability are either conservative and relatively easy to test [1]- [4], or they are necessary and sufficient conditions but NP hard to test PI 7 vi , 191. This paper attempts to close the gap between existing N P hard necessary and sufficient stability conditions and conservative sufficient stability conditions. This is achieved by deriving sets of sufficient conditions as well as sets of necessary conditions, thus tightly bounding the actual stability region.…”

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confidence: 99%

Stability of first order discrete time systems with time-variant communication delays in the feedback path

Lorand

Sichitiu²,

Bauer³

et al.

IEEE APCCAS 2000. 2000 IEEE Asia-Pacific Conference on Circuits and Systems. Electronic Communication Systems. (Cat. No.00EX394

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This paper addresses the problem of stability in 1st order systems with time-variant communication delays in the feedback path. Sets of necessary and sets of SUA;-cient conditions are obtained and resulting stability regions are shown. I. IntroductionData networks play an increasingly important role in the development of technology in the 21St century.With improved access to high speed data networks, many engineering systems will be embedded in networks that can support fast feedback loops. This paper takes a close look at the simple case of a first order system with proportional feedback through a communication network. The problem of stability in discrete time systems with time-variant delay has been addressed in only a few publications [1]-[4], even though its importance is rising rapidly. The derived conditions for stability are either conservative and relatively easy to test [1]-[4], or they are necessary and sufficient conditions but NP hard to test PI 7 vi , 191.This paper attempts to close the gap between existing N P hard necessary and sufficient stability conditions and conservative sufficient stability conditions. This is achieved by deriving sets of sufficient conditions as well as sets of necessary conditions, thus tightly bounding the actual stability region. Time variant delays in discrete-time systemsA. The nature of a discrete time-variant delay One important characteristic of time-variant discrete delays is that it maps a countable sequence of input values into a countable sequence of sets of output values. Hence, the output set of a time-variant discrete delay operator can contain zero, one or several values.For this reason, it is necessary to add an interface at the delay output. We can distinguish between two components of a time-variant linear network connection: a delay introduced by the communication link, (i.e. the delay itself) and the interface that connects the network to the system at the receiving end. Figure 1 shows the two components of the time-variant linear network connection. The input and the output of the time-variant delay d(n) are the sample sets u(n) and U ( . ) . The symbol n describes discrete time with respect to an arbitrary sampling period. The sets U ( . ) and v(n) describe all input/output samples (scalar or otherwise) that are entering or leaving the block d(n) within a sampling period, i.e. between time instant n-1 and time instant n. The output signal is a sequence of sets satisfying the following relation: Figure 1: A discrete time-variant delay We will use the following notation: 0 M ( n ) : The cardinality of the input u(n) at time n; 0 N ( n ) : The cardinality of the output v(n) at time instant n; 0 d ( n ) : a function d : Z+ -+ Z+ where 2, is the set of nonnegative integers satisfying the inequality The function d ( n ) represents the delay the communication link introduces at time instant n for the input U ( . ) .

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Exponential stability of discrete time uncertain systems with time-varying delay

Cited by 14 publications

References 9 publications

A new exponentially stable sliding mode control approach for a class of uncertain discrete systems with time delay

A new exponentially stable sliding mode control approach for a class of uncertain discrete systems with time delay

New Conditions for the Exponential Stability of Pseudolinear Difference Equations in Banach Spaces

Stability of first order discrete time systems with time-variant communication delays in the feedback path

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