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Zbl 1197.34160
Balasubramaniam, P.; Manivannan, A.; Rakkiyappan, R.
Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters. (English)
[J] Appl. Math. Comput. 216, No. 11, 3396-3407 (2010). ISSN 0096-3003

Summary: This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequalities (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems. The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by the Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

MSC 2000:: *34K50 Stochastic delay equations
34K40 Neutral equations
34K20 Stability theory of functional-differential equations

Keywords: Markovian jumping parameters; global exponential stability; linear matrix inequality; Lyapunov-Krasovskii functional; generalized eigenvalue problems

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Zentralblatt MATH Berlin [Germany]