Stability analysis of linear continuous-time delay-difference systems with multiple time-delays

Strong Stability Analysis of Linear Delay-Difference Equations With Multiple Time Delays

“…The results are recorded in Table I. It can be seen that γ1 obtained by Theorem 1 with k = 2 is smaller than the one obtained by the results in [12], [14] and is the same as the one obtained from (2) and the one obtained by Theorem 1 in [29]. It follows from Table I that Theorem 1 with k = 2 allows us to obtain much less conservative results than that in [12] and [14].…”

“…We conclude that LMI (9) in Theorem 1 is related to searching for an integral Lyapunov functional in the form of (29). Note that there is no assumption on the positivity of Q k,l , l = 1, 2, .…”

“…Remark 2: Following the idea in [29], the convergence rate analysis of (1) can be performed by replacing Ai, i = 1, 2, . .…”

“…where γ1 ∈ R is a free parameter to be determined. Similarly to Example 1, we use Theorem 1, Theorem 1 in [29], Theorem 4 in [14], Theorem 6.1 in [12] to determine the minimum γ1 such that delay-difference equation ( 1) is strongly stable. The results are recorded in Table I.…”

“…The conditions in [25] rely on computing the coefficients of the characteristic function and are thus not explicitly expressed as a function of the coefficient matrices, which makes their use for robust stability analysis more difficult. The stability of (1) has also been studied via Lyapunov-Krasovskii functionals (LKF), leading to sufficient conditions in terms of LMIs, see [12], [14], [16], [29], [32] and [33]. In [27] an internally positive representation approach was introduced to such a system, resulting in a delay-independent sufficient condition.…”