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

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.

### MSC:

 34K20 Stability theory of functional-differential equations 34K40 Neutral functional-differential equations
Full Text:

### References:

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