Note on stability of discrete-time time-varying delay 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) …”

Improved Stability Criteria on Discrete- time Systems with Time- varying and Distributed Delays

“…[20] For the symmetric appropriate dimensional matrices R > 0, Ξ, matrix Γ, the following two statements are equivalent: 1) Ξ − Γ T RΓ < 0; 2) there exists a matrix of appropriate dimension Λ such that…”

“…Then by utilizing the definition of Schur-complement, the inequalities in (20) and (21) can be equivalent to the LMIs in (18) and (19) through setting µ = ρ −2 and ν = υ −2 . Remark 3.…”

“…networked control system [16] , descriptor system [17] , Lur e system [18] , and neural networks [22] . Recently, by utilizing some developed techniques such as reciprocal convex technique, some less conservative results have been given, as compared with these previous ones [19,20] . Furthermore, since the delay-partitioning idea is efficient in reducing the conservatism, this idea and improved one were also used to study the stability for discrete-time systems, and the conservatism can be greatly reduced by thinning the delay intervals [21,22] .…”

Singular Distributed Parameter System Iterative Learning Control with Forgetting Factor with Time- Delay

“…Time-delay occurs in various physical, industrial and engineering systems such as biological systems, neural networks, networked control systems, multi-agent systems, and so on [5][6]. It is well known that the existence of timedelay is source of proof performance and instability of dynamic systems [7][8].…”