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Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations. (English) Zbl 1065.34076

This paper is concerned with the asymptotic stability of the delay differential systems of neutral type \[ x'(t) - C x'(t-\tau_2)= A x(t) + B x(t-\tau_1)+ f_1(t,x(t))+f_2(t,x(t-\tau_1), \quad t \geq 0, \tag \(*\) \] where \( \tau_1, \tau_2\) are positive constant delays, \( A,B,C\) constant real matrices of appropriate dimensions, and the nonlinear functions \( f_i\) satisfy \( \| f_i(t,u) \| \leq \alpha_i \| u \|\), \(i=1,2\), for some scalars \( \alpha_i\). For system \((*)\), the author gives sufficient conditions on the matrix coefficients that imply the asymptotic stability of the zero solution. The main advantage of the present result is that the sufficient conditions for stability can be checked by means of a convex optimization algorithm whereas other stability criteria are expressed in terms of matrix norms and turn out to be more conservative. Some examples of two-dimensional problems are presented in which the stability is tested by using Matlab’s LMI Control Toolbox.

MSC:

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

Software:

LMI toolbox; Matlab
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References:

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