A piecewise analysis method to stability analysis of linear continuous/discrete systems with time‐varying delay

Abstract

SUMMARYThe delay-dependent stability problem of linear continuous/discrete systems with time-varying delay is investigated based on a piecewise analysis method (PAM). In the method, the variation interval of the time delay is firstly divided into several subintervals. By checking the variation of the Lyapunov functional in every subinterval, some new delay-dependent stability criteria are derived. Several numerical examples show that our method can lead to much less conservative results than those in the existing references. Moreover, when the number of the divided subintervals increases, the corresponding criteria can provide an improvement on the results.

Stability of Discrete-Time Systems with Time-Varying Delay: Delay Decomposition Approach

“…Using these methods, many stability criteria were derived by checking a variation of LKF in a whole interval of the time-delay. Contrary to this approach, in [24,25], in order to obtain some less conservative stability conditions, the interval of the time delay is divided into multiple equidistant subintervals and interval delay-dependent LKF (ID-D LKF) is constructed. By checking the variation of the ID-D LKF defined on the subintervals, some new delay-dependent stability criteria are derived.…”

“…It is shown that the presented stability condition is much less conservative than the existing ones [1, 2, 6-9, 13-15, 22, 24], because it has a lower value of MAUB. The derived condition can be seen as an extension of the methods in [24,25], wherein the whole delay range is divided to n ≥ 2 equal subintervals. As the number of subintervals in [24,25] is greater than two, the decomposition approach is more complex and the resulting stability conditions are more conservative and difficult to implement.…”

“…The derived condition can be seen as an extension of the methods in [24,25], wherein the whole delay range is divided to n ≥ 2 equal subintervals. As the number of subintervals in [24,25] is greater than two, the decomposition approach is more complex and the resulting stability conditions are more conservative and difficult to implement. To demonstrate the effectiveness of the proposed method, numerical examples are given in section 3.…”

Delay Dependent Stability of Time-delayed Linear Systems using New Structure of L-K Funciton

“…[4], 변수추가 [10], 영(zero) 더 미(dummy) 함수 추가 [5], 그리고 구간 분할 [3] [7][8]등이 있 다. 이중 구간분할은 시간지연을 개의 부구간으로 나누고, …”

Robust stability of linear uncertain discrete-time systems with interval time-varying delay

“…Yue et al [18] divided the variation interval of the time-delay into subintervals and employed a different LKF in every subinterval to derive some stability criteria for linear discrete-time systems with time-varying delay. Chen and Fong [19] converted the discrete-time system into an augmented one and developed some stability conditions that do not require the assumption of stability of the system when the delay vanishes to 0.…”