Stability for composite singular systems of differential equations with a delay (Q2563548)

The authors consider the following singular system of differential equations with a delay \[ A\dot x(t)= Bx(t)+Cx(t-\tau),\tag{1} \] where \(x(t)\in\mathbb{R}^n\), \(A,B,C\in\mathbb{R}^{n\times n}\), \(\text{det }A=0\), \(\tau>0\) is a constant. An exponential estimate for the solution of (1) and a comparison inequality for the systems are established, and the criteria for asymptotic stability for the composite singular system are given.