Stability criteria for linear time-invariant systems with multiple delays (Q1840813)

The author investigates the stability of the time-invariant system with multiple delays \[ x'(t)= A_0x(t)+ \sum^r_{k=1} A_k x(t- \tau_k),\quad t\geq 0. \] Here, \(x\in\mathbb{R}^n\), \(A_k\in \mathbb{R}^{n\times n}\), \(\tau_k> 0\). Two results are deduced for delay-dependent \(\alpha\)-stability and delay-independent asymptotic stability, respectively. Each of the results involves only one tuning parameter matrix \(P> 0\).