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Robust Stability Analysis For Uncertain Time-Delay Lur’e System

Posted on:2015-10-11Degree:DoctorType:Dissertation
Country:ChinaCandidate:W Y DuanFull Text:PDF
GTID:1108330482969716Subject:Control Science and Engineering
Abstract/Summary:PDF Full Text Request
Lur’e system is a class of nonlinear system, which consists of a feedback connection of a linear dynamical system and a nonlinearity satisfying the sector condition. Lur’e system has a strong application background in engineering practice, which leads that to be emphasised heavily. Meanwhile, time delays are commonly encountered in the control loops and are often attributed as a source of poor performance and instability of systems. Basing on the basic concepts and methods of the control theory, the robustly absolute stability for a class of neutral-type Lur’e systems with time-varying delays and sector-bounded nonlinearities is deep studied in the dissertation. The main results of the dissertation are summarized in the following:1. The absolute and robustly absolute stabilities for a class of uncertain neutral-type Lur’e systems with time-varying delays are considered. The time-varying delays are continuous-time and differentiable functional with the lower bound of zero. By discretizing the delay interval into two segmentations with an equal width, new delay-dependent sufficient conditions for the robustly absolute stability of neutral-type Lur’e systems are proposed in terms of LMI via a modified Lyapunov-Krasovskii functional approach. These conditions reduce the conservativeness of the present results.2. The robustly absolute stability for a class of uncertain neutral-type Lur’e system with interval time-varying delays is considered. Firstly, when the lower bound of the time-derivative of the time-delay is unknown, some new robustly stable criteria are proposed in terms of LMI via a modified Lyapunov-Krasovskii functional approach by using the general free-weighting matrix method and a piecewise analysis method. Secondly, when the lower bound of the time-derivative of the time-delay is known, by dividing the delay interval into two time-varying segmentations with a selectable width, some new delay-derivative-dependent stable criteria are derived. The criteria proposed here are less conservative than the existing ones.3. The robustly absolute stability for a class of uncertain Lur’e system with multiple time-varying delays is considered. Some LMI-based delay-dependent robustly absolutely stable criteria are derived via a modified Lyapunov-Krasovskii functional approach. Moreover, when the multiple delays are time-invariant, less conservative delay-dependent robustly stable criteria than those recently proposed are also obtained by discretizing the whole delay interval into two segmentations with a selectable width.4. The robustly absolute stability for uncertain discrete-time Lur’e systems with interval time-varying delays is considered. Both the cases with time-invariant and time-varying nonlinearities are studied. By dividing the variation interval of the time-delay into some subintervals, some new delay-range-dependent robustly stable criteria, which are less conservative than the existing ones, are derived in the form of LMI via a modified Lyapunov-Krasovskii functional approach.5. The synchronization problem for a class of Lur’e type complex dynamical networks with time-varying delays is considered. Based on an Lyapunov-Krasovskii functional, some new delay-dependent synchronization criteria, which are less conser-vative than the existing ones, are derived in the form of LMI by employing the delay decomposition and the free-weighting matrix methods. And a strategy for synchro-nization is presented based on a linear feedback controller.
Keywords/Search Tags:Neutral-type Lur’e system, Discrete-time Lur’e system, Delay decompo- sition, Delay-dependent criterion, Robust stability, Linear matrix inequality
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