Abstract
The problem of absolute stability analysis for neutral-type Lur’e systems with time-varying delays is investigated. Novel delay-decomposing approaches are proposed to divide the variation interval of the delay into three unequal subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on the obtained subintervals. The integral inequality method and the reciprocally convex technique are utilized to deal with the derivative of the LKFs. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). Compared with some previous criteria, the proposed ones give the results with less conservatism and lower numerical complexity. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.
Highlights
Over the last 30 years, time delay system has been one of the hottest research areas in control engineering for time delay often appears in many control systems either in the state, the control input, or the measurements [1, 2]
Since time delay frequently occurs in practical systems and is often the source of instability, there have been many results for stability of delayed systems [3,4,5,6,7,8,9]
Stabilization [10,11,12], filtering [13], and adaptive control [14] of time-delay systems have received considerable attention. e neutral systems often appear in the study of automatic control, population dynamics, and vibrating masses attached to an elastic bar [15]
Summary
Over the last 30 years, time delay system has been one of the hottest research areas in control engineering for time delay often appears in many control systems either in the state, the control input, or the measurements [1, 2]. To avoid involving a considerable number of free-weighting matrices and leading to a computationally expensive stability criterion in [26], the general free weighting matrix method was proposed and some improved delay-range-dependent stability criteria were obtained [27, 28]. By constructing a LKF including both double-integral terms and triple-integral terms, using the piecewise analysis method, Wirtinger-based integral inequality, and the reciprocally convex combination technique, some new stability criteria were obtained in [35]. tt+θ xT(s)Q dsdθ had to be introduced into the derivation process in [35], which leads to a sharp increase in the dimensions of the LMIs involved Motivated by this mentioned above, the aim of this work is to revisit the stability analysis for the neutral-type Lur’e system.
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