Another sufficient condition for the stability of grey discrete-time systems

Stability Condition for Discrete Interval System with Time-Varying Delay Time

“…이들 연구는 시스템의 행렬이 시불변인 경우에는 주로 고유치(eigenvalue)의 성질을 이용 [9]- [13]하여 안정 조건 이 유도되었으나, 구간시스템이 아닌 경우에 대하여 리아프노 프(Lyapunov)안정 이론을 이용한 결과 [7]에 비하여 한계가 있 다. 고유치 성질을 이용한 기존의 결과들은 시불변 지연시간을 갖는 구간시스템에만 적용가능한 안정조건으로 스펙트랄 노름 (spectral norm) [1], [7], 스펙트랄 반경(spectral radius) [9], [11], [13]과 특정한 행렬의 요소 값을 이용한 간단한 부등식 [4], [7]에 비하여 매우 간단하게 표현된다. 또한, 시불변 지 연시간에만 적용가능한 기존의 결과들 [1], [6], [7], [13] (1) …”

Robust regional eigenvalue‐clustering analysis for grey discrete‐time systems with/without state delay

“…That is, the proposed sufficient conditions in (40a,b) are the special cases of the proposed sufficient conditions in (36a,b). Next, the proposed sufficient condition (40a) is compared with condition (37) given by Liu and Shyr [5] and by Shyr and Hsu [6]. Equations (38) …”

“…The stability of grey linear discrete-time systems has already been discussed in studies such as Zhou and Deng [4], Liu and Shyr [5] and Shyr and Hsu [6]. However, an unresolved issue is that, to achieve robust and consistent performance, the eigenvalues of a dynamic system must remain within a specified region.…”

“…Kang et al [26] focused on the problem of pole-assignment within a specified circular region of a grey discrete-time system with state delay. In the special case of eigenvalue-assignment inside the unit circle, the solution proposed by Kang et al [26] were further refined by Liu and Shyr [5] and by Shyr and Hsu [6]. Here, it should be noted that (i) in the absence of state delay, the conditions proposed by Liu and Shyr [5] and by Shyr and Hsu [6] are less conservative than those proposed by Zhou and Deng [4] and by Liu [23]; (ii) in the presence of state delay, the conditions proposed by Liu and Shyr [5] and by Shyr and Hsu [6] are less conservative than those proposed by Liu [25].…”

“…Firstly, applying the approach developed by Liu and Shyr[5] and by Shyr and Hsu[6] obtains j=1 ε aijφij ≤ 0.22273 < 1, for ε a11 ∈ −0.5, 0 , ε a12 ∈ −0.18, 0 ,…”