On estimates of solutions to systems of differential equations of neutral type with periodic coefficients (Q486365)

The paper deals with neutral system of differential equations of the form \[ \frac{d}{dt}(y(t)+Dy(t-\tau))=A(t)y(t)+B(t)y(t-\tau),\,\,\,t>0, \] where \(D\) is a constant \(n\times n\) matrix, \(\rho(D)<1\), \(A(t)\) and \(B(t)\) are continuous \(T\)-periodic \(n\times n\) matrices and \(\tau>0\) is the delay. Sufficient conditions are given for the exponential stability of the zero solution. Moreover, exponential estimates of the norm of solution of the problem \[ y(t)=\varphi(t),\,\,\,t\in[-\tau,0],\,\,\,y(0^+)=\varphi(0), \] where \(\varphi\in C^1[-\tau,0]\), are derived.