Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay

Xu, Shengyuan; Lam, James; Yang, Chengwu

doi:10.1016/s0167-6911(00)00113-4

Cited by 164 publications

(65 citation statements)

References 17 publications

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“…Remark 2 The structure of the parameter uncertainties in (5)-(6) has been widely used for the robust control and robust observer problems for both the discretetime and the continuous-time systems, which can represent many practical situations [32,33].…”

Section: Assumptionmentioning

confidence: 99%

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

2011

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The robust observer problem is considered in this paper for a class of discrete-time neural networks with Markovian jumping parameters and modedependent time delays which are in both discretetime form and finite distributed form. The neural network switches from one mode to another controlled by a Markov chain with known transition probability. Time-delays considered in this paper are modedependent which may reflect a more realistic version of the neural network. By using the Lyapunov functional method and the techniques of linear matrix inequalities (LMIs), sufficient conditions are established in terms of LMIs that ensure the existence of the robust observer. The obtained conditions are easy to be verified via the LMI toolbox. An example is presented to show the effectiveness of the obtained results.

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Section: Assumptionmentioning

confidence: 99%

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

2011

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“…The parameter uncertain structure in (5) and (6) has been widely studied in the issues of robust control and filtering for uncertain systems; see, e.g., [17,22]. It comprises the 'matching conditions', and many physical systems can be either exactly modeled in this manner or overbounded by (6).…”

Section: Remarkmentioning

confidence: 99%

“…Lemma 4 [22] Let D, E and F be matrices with appropriate dimensions. If F T F ≤ I , then for any scalar ε > 0, we have…”

Section: Lemmamentioning

confidence: 99%

Robust l 2−l ∞ Guaranteed Cost Filtering for Uncertain Discrete-Time Switched System with Mode-Dependent Time-Varying Delays

Zong

Hou

2010

Circuits Syst Signal Process

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This paper deals with the problem of robust l 2 − l ∞ guaranteed cost filtering for uncertain discrete-time switched systems with both mode-dependent timevarying delays and norm-bounded parameter uncertainties. The objective of this paper is to design a stable guaranteed cost filter which guarantees that the error system is asymptotically stable and the cost function value is not more than a specified upper bound for all admissible uncertainties. By resorting to a descriptor system approach, delay-dependent sufficient conditions of guaranteed cost filtering are presented in terms of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed algorithms.

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“…The properties of difference equations, especially the stability and stabilization, were studied by many researchers, see [1][2][3][4][5][6] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Impulsive stabilization of delay difference equations and its application in Nicholson's blowflies model

Ding

2012

Adv Differ Equ

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In this article, we consider the impulsive stabilization of delay difference equations. By employing the Lyapunov function and Razumikhin technique, we establish the criteria of exponential stability for impulsive delay difference equations. As an application, by using the results we obtained, we deal with the exponential stability of discrete impulsive delay Nicholson's blowflies model. At last, an example is given to illustrate the efficiency of our results.

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Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay

Cited by 164 publications

References 17 publications

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

Robust l 2−l ∞ Guaranteed Cost Filtering for Uncertain Discrete-Time Switched System with Mode-Dependent Time-Varying Delays

Impulsive stabilization of delay difference equations and its application in Nicholson's blowflies model

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