An exact LMI condition for the strong delay‐independent stability analysis of neutral delay systems

Abstract

Summary This paper concentrates on strong delay‐independent stability of neutral linear time‐invariant delay systems with multiple commensurate time delays. The stability analysis of linear neutral systems is complicated by the need to locate the roots of a transcendental characteristic equation and to take into account the global hyperbolicity of an associated difference system. In this paper, we propose a convex necessary and sufficient condition for testing strong delay‐independent stability. This result mainly follows from Kronecker sum properties and the Kalman‐Yakubovich‐Popov lemma, which allows us to present the main result in terms of a single linear matrix inequality feasibility test. The paper is closed by showing numerical examples that illustrate the applicability and effectiveness of the proposed method.

A survey of inequality techniques for stability analysis of time‐delay systems

“…After simple arrangements, the inequality (28) is obtained from the above inequality (30). Moreover, when the value of N is sufficiently large, one has…”

“…[15][16][17][18] Stability is a fundamental issue for time-delay systems, which has been extensively investigated during the last decades. [19][20][21][22][23][24][25][26][27][28][29][30][31] There are two main approaches to stability analysis of time-delay systems: frequency-domain approach and time-domain approach. In frequency-domain approach, the eigenvalues of a system matrix are calculated to study the stability of time-delay systems.…”

“…Stability is a fundamental issue for time‐delay systems, which has been extensively investigated during the last decades 19‐31 . There are two main approaches to stability analysis of time‐delay systems: frequency‐domain approach and time‐domain approach.…”

H∞ robust control for underwater supercavitating vehicle with time delay

“…As for time-delay system control, there are some mature methods, such as PID classical control method (Das, 2020) (Nie et al, 2020) and other advanced control methods. Advanced control methods include Smith prediction (Mateusz and Krzysztof, 2018), predictive control (Zhou et al, 2019), linear matrix inequality method and robust control (Jong and Hong, 1999; Fernandode et al, 2018; Sedova and Pertseva, 2019; Souza, 2018; Arceo, 2018; Meng et al, 2015; Vembarasan et al, 2014), etc. PID controller is a classical control method for time-delay systems.…”