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Rakkiyappan, R.; Balasubramaniam, P.; Krishnasamy, R.

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations. (English) Zbl 1211.34087

J. Comput. Appl. Math. 235, No. 8, 2147-2156 (2011).
Summary: Consider the following neutral system with mixed time-varying delays and nonlinear perturbations:
\[ \begin{aligned}& \dot x(t)=Ax(t)+Bx(t-\tau(t))+C\dot x(t-h(t))+f_1(x(t),t)+f_2(x(t-\tau(t)),t)+f_3(\dot x(t-h(t)),t),\\ & x(\theta)=\phi(\theta),\quad \dot x(\theta)=\varphi(\theta)\quad \forall\theta\in[-\max(\overline h,h_2),0]\end{aligned} \]
where \(x(t)\in\mathbb R^n\) is the state vector, \(A,B,C\in\mathbb R^{n\times n}\) are constant matrices, \(h(t)\), \(\tau(t)\) are the neutral delay and the time-varying discrete delay, respectively, and they are assumed to satisfy
\[ \begin{aligned} & 0\leq h(t)\leq \overline h\quad \dot h(t)\leq h_d,\\ & h_1\leq\tau(t)\leq h_2,\quad \dot \tau(t)\leq \mu,\end{aligned} \]
where \(\overline h,h_d,h_1,h_2\) and \(\mu\) are constants.
A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Cited in 26 Documents

MSC:

34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations

Keywords:

linear matrix inequality; Lyapunov-Krasovskii functional; neutral systems; nonlinear perturbation
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\textit{R. Rakkiyappan} et al., J. Comput. Appl. Math. 235, No. 8, 2147--2156 (2011; Zbl 1211.34087)
Full Text: DOI

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