Improved stability criteria for linear systems with time-varying delay

Improved linear matrix inequality approach to stability analysis of linear systems with interval time-varying delays

“…where, was used in [24] and [25]; but, it was not involved in the definition of augmented vector. Second, unlike [25], the state ‫ݔ‬ is imported in the integrand of the triple-integral term.…”

“…in Theorem 1 are solved and the corresponding maximum allowable values of ߟ ଶ for different values of ߟ ଵ are computed and compared to the rival methods.Table 1clearly shows that the proposed approach outperforms the methods presented in[11],[21],[22],[23],[25] and [27].Table 1.MADBs computed from the different design methods for Example 1 Example 2. Consider the following closed-loop control system with time-varying delay taken from [26]:…”

“…3 3 In [24], triple-integral terms were incorporated in the LKF to improve stability condition for the constant time-delay systems. Inspired by [24], triple-integral terms were employed to extract better stability criterion for linear systems with time-varying delay [25,26]. A new LKF which includes the information of the timevarying delay is constructed in [27], to extract delay-range-dependent robust stability measure for uncertain systems with interval time-varying delay based on an integral inequality approach.…”

A new delay-distribution-dependent robust stability criterion for uncertain systems with time-varying delay

“…Delaydependent criteria are generally less conservative than delayindependent ones. In order to reduce the conservativeness of the robust stability and stabilization criteria, many methods have been proposed, such as the model transformation method [3]- [5], augmented Lyapunov-Krasovskii functional method [6]- [9], free weighting matrices method [10]- [12] and delay-partitioning method [13]- [15]. Recently, several stability criteria (i.e., [16,Theorem 1], [17,Theorem 1], [18,Theorem 1], [19,Theorem 1] and [20, Theorem 1, ii)]) obtained by different methods have been proved in theory to have the same solvability in [20], and further, a less conservative stability criterion is provided in [20] by using delay-partitioning method.…”

“…The inequality(9) in Lemma 3.3 is feasible if and only if the inequality (10) in Theorem 4.1 is feasible. Proof…”