Asymptotic Stability Analysis of Linear Time- Delay Systems: Delay Dependent Approach

Time delayed system stability theory in the sense of non-Lyapunov delay independent and delay dependent approach: New results

“…The counterexamples, based on the proposed approach, supported by the application of the Lambert function, are given in [14][15][16][17]. Remark 2.…”

“…Substituting a matrix variable R by scalar variable s in (60), the characteristic equation of the system (6) is obtained as: These matrix conditions are analogous to the following known scalar condition of asymptotic stability: System (6) is asymptotically stable if and only if the condition Re 0 s < holds for all solutions s of (63)as in [14][15]. Remark 7.…”

“…Remark 4.The necessary condition of Lemma 2 is derived directly from the proof of Theorem 2 in[13] and[14].Theorem 10. Suppose that there exist(s) the solution(s) Remark 5.…”