Unconditional stability for certain delay differential equations (Q2785863)

The author obtains sufficient conditions for the unconditional stability of the zero solution of \((n+1)\)th-order linear delay-differential equations of the form NEWLINE\[NEWLINE\omega^{(n+1)}(t)= \alpha\sum^n_{i=0} a_{n-i}w^{(i)}(t)+ (1-\alpha)\sum^n_{i=0} a_{n-i}w^{(i)}(t-\tau),\tag{\(*\)}NEWLINE\]NEWLINE where \(\tau>0\) is constant and \(0\leq\alpha\leq 1\). It may be recalled that the zero solution of \((*)\) is said to be unconditionally stable if, for any \(\tau\geq 0\), the zero solution is asymptotically stable. Several examples are given to illustrate the results obtained.