Absolutely exponential stability of Lur’e distributed parameter control systems

Wirtinger-Type Inequality and the Stability Analysis of Delayed Lur'e System

“…Remark 1. Different from previous work [6,9,10,12,15], in this paper, by using the convex expression ( ( )) = Λ ( ( )) ( ), we transform the original nonlinear system (1) into a linear uncertain system (6). As a result, the stability problem of nonlinear Lur' e system (1) can be transformed into the robust stability problem of linear uncertain system (6).…”

“…Therefore, the stability analysis of delayed Lur' e system becomes very important. Up to now, various stability conditions have been obtained, and many excellent papers and monographs have been available (see [7][8][9][10][11][12]).…”

Improved Control of Distributed Parameter Systems with Time-Varying Delay Based on Mobile Actuator-Sensor Networks

“…Therefore, time delays are considered in order to better reflect the reality in the distributed parameter systems. However, delays may destabilize the systems, so the stability and control probelm for distributed parameter systems with time delays have been intensively studied in the recent years (Luo, Xia, Liu & Deng, 2009;Fridman & Orlov, 2009;Fridman, Nicaise & Valein, 2010;Tai & Lun, 2012). For example, the exponential stability of DPS with time-varying delays was investigated in Fridman and Orlov (2009), and several sufficient conditions for exponential stabilization were given by using different Lyapunov functions and linear matrix inequality.…”

On the asymptotic hyperstability of switched systems under integral-type feedback regulation Popovian constraints

“…On the other hand, the topics of absolute stability and hyperstability are of a very relevant interest even nowadays because of their theoretical importance and its wide range of applications including stabilization under parametrical dispersion of regulator components either in the absence or in the presence of delays, hybrid mixed continuous-time and digital systems or passivity issues. See, for instance, some recent related background in Braverman & Zhukovskly (2012), Chen et al (2011), Duarte-Mermoud et al (2012), Song & Cao (2008), Tai (2012), Tai & Lun (2012), Zhou et al (2009) and references therein. Also, the property of absolute stability has been also investigated for systems involving timedelays; see, for instance, Wu et al (2009) and references therein.…”