Delay-dependent robust absolute stability of uncertain Lurie singular systems with neutral type and time-varying delays
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ORIGINAL ARTICLE
Delay-dependent robust absolute stability of uncertain Lurie singular systems with neutral type and time-varying delays Yuechao Ma1 · Pingjing Yang1 · Qingling Zhang2
Received: 13 March 2016 / Accepted: 29 April 2017 © Springer-Verlag Berlin Heidelberg 2017
Abstract This paper is concerned with the robust absolute stability analysis for Lurie control of the neutral singular systems. By using Lyapunov–Krasovskii function method, delay dependent criteria for absolute stability of system are derived in terms of Linear Matrix Inequality. The difference between this paper and other existing results is that the lower bounds and upper bounds of discrete-delay are considered, which will obtain some less conservative stability analysis results. Finally, some numerical examples are presented to illustrate the effectiveness of the method. Keywords Lurie singular systems · Neutral type · Absolute stability · Delay-dependent · Linear matrix inequalities
1 Introduction A great number of nonlinear systems in engineering, such as neural networks, vehicle suspension systems, automatic control etc, can be modeled as Lurie control systems whose nonlinear element satisfies certain sector constraints [1–7]. Moreover, the notion of absolute stability was introduced by Lurie [1] for the plant of automatic pilot in the 1940s, is one of the oldest open problems in the theory of stability. Since that, absolute stability analysis for the Lurie systems has been extensively studied in [2–7]. For example, Gao * Pingjing Yang [email protected] 1
College of science, Yanshan University, Qinhuangdao 066004, Hebei, People’s Republic of China
2
College of Science, Northeastern University, Shenyang 110004, Liaoning, People’s Republic of China
et al. [3] considered the absolute stability analysis for timedelay Lurie control systems with nonlinearity located in a finite sector. On the other hand, the time delay is frequently viewed as a source of instability and encountered in various engineering systems such as chemical processes, long transmission lines in pneumatic systems, networked control systems etc [8–14]. Many researchers have investigated the absolute stability of Lurie control systems with time-delays and derived some stability criteria [9, 10, 12, 13], but most of the existing criteria are delay-independent. It limits the applicable ranges of those results. Generally speaking, the conservativeness of delay-dependent criteria is smaller than the delay-independent. To avoid this, we will give delaydependent absolute stability criteria. On the other hand, singular control systems have been extensively studied in the past years due to the fact that singular systems better describe physical systems than regular ones. A large number of results based on the theory of the regular systems have been extended to the area of singular systems [15–24]. Recently, the stability of Lurie singular systems has been considered [16–20]. Yang [18, 19] discussed the problem of the stability of the Lure singular system, but he d
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