Reciprocally convex approach to stability of systems with time-varying delays

By PooGyeon Park, J. Ko, C. Jeong. at - Automatisierungstechnik, 2011

2,675 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/e46be7cb12666e6e161f2a176778b2d676750bbc

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Citations in the corpus

Novel delay‐derivative‐dependent stability criteria using new bounding techniques (2013, methodology): “is proposed in [13] to estimate some related integral terms.”
Reliable mixed passive and ℋ∞ filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures (2015, background): “On the other hand, in view of the reciprocally convex approach proposed in [49], it is not difficult to find from (17) that”
Hierarchy of LMI conditions for the stability analysis of time-delay systems (2015, background): “The second one remains in the use of technical lemmas to provide tight inequalities [14, 15, 18, 23].”
Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay (2016, background): “Lemma 6 (Reciprocal convexity lemma [8]) For any vector 2 R, matrices R1; R2 2 SC n , S 2 R , W1; W2 2 R , and real scalars ̨ > 0; ˇ > 0 satisfying ̨ C ˇ D 1, the following inequality holds:”
New insight into delay‐dependent stability of time‐delay systems (2015, methodology): “The stability conditions in [19, 32, 33] are derived for linear systems with time-varying delays.”
Event-Triggered $H_\infty$ Load Frequency Control for Multiarea Power Systems Under Hybrid Cyber Attacks (2019, background): “Lemma 2 [50]: Suppose that there exists a matrix N ∈”
Switching-Like Event-Triggered Control for Networked Control Systems Under Malicious Denial of Service Attacks (2020, background): “…deal with one cross item in ˙ V 3 ( t ) , we have The another cross item in ˙ V 3 ( t ) can be written as Then,by usingreciprocally convex approach [28]todeal with two cross items in (18), if there exist Furthermore, taking the ﬁrst event-triggered scheme in (7) and z T ( t ) z ( t ) ≤ γ 2 w T ( t…”
Filtering of Markovian Jump Delay Systems Based on a New Performance Index (2013, methodology): “Lemma 1 ([25], [29]): Consider system (9) with satisfying .”
Relaxed results on reachable set estimation of time‐delay systems with bounded peak inputs (2016, methodology): “These conditions are derived by using the Jensen’s inequality [24] together with the reciprocally convex approach [26].”
Optimal partitioning method for stability analysis of continuous/discrete delay systems (2015, methodology): “Based on the idea, new Lyapunov functionals are constructed, and the reciprocally convex approach proposed in [3] is employed to deal with the delay in each subinterval.”