Lur'e system is a class of typical nonlinear system that nonlinear terms are constrained in the finite Hurwitz sector or infinite Hurwitz sector. Almost of all real Lur'e systems may suffer uncertainties in different forms, such as unmodeled dynamics, structured parametric uncertainties, change of the operating environment, model reduction and linearization approximations and external disturbances uncertainties, etc. Usually, these uncertainties are measurable and can be restricted in some range. Robust control theory is an effective way to deal with the control problems with the uncertain systems. On the other hand, quite a number of practical systems with numerous dimensions may have some fast variables taking on singular impulse characteristic, such as electric power system, control system of rolling mill assembly, biochemical process, nuclear reactor, control system of airplane and rocket, and chemical diffused reaction, etc. So, it is important to study the problem of robust control of singular system in the domain of control theory. Moreover, large-lag links, transmission process and complicated on-line analyzer etc, are common in the number of industrial processes, which can cause delay in the systems. Such delays will be a main cause of bad performance or even instability for control systems. Therefore, it is found that the problems of robust control for uncertain Lur'e system included time-delays must been fully investigated due to the fact that all above phenomena may occur in the real control systems.In this paper, the problems of robust control for uncertain Lur'e system with time-delays have been studied. The idea of research rooted in the state system and semistate (singular) system. For state systems and semistate (singular) system, respectively, the problems of robust stability and the design of robust controller have been investigated based on Linear Matrix Inequality (LMI), according to Lyapunov-Razumikhin stability and convex optimization theory, and Barbalat's Lemma and nonsingular linear transformation of model reduction, respectively. The main contents of this paper are outlined as follows,1 The new absolute stability and stabilization conditions for a class of Lur'e uncertain time-delay systems are proposed through introducing a new state transformation. The result shows that there has been a distinct amelioration in conservation, in comparison with the reported results.2 The problems of robust stability and robust H# control for a class of Markovian Lur'e jumping system are studied. The sufficient conditions to guarantee robust exponential stability for the closed-loop systems are obtained based on Linear Matrix Inequality, moreover, the approach of design of robust H# output feedback controller is introduced.3 The problem of reliable H# control for a class of Lur'e systems with polytopic uncertainties is studied when all control components are operational as well as when some control components experience failures, the design approach of reliable H# controller is also obtained.4 Considering a class of uncertain Lur'e singular system with time-delays, the problem of robust stability is investigated based on Barbalat's Lemma and nonsingular linear transformation of model reduction. Furthermore, the approach of design of robust H# state feedback controller is also introduced.5 For a class of uncertain Lur'e singular system with time-delays and saturating actuators, the delay-dependent sufficient conditions of robust stability and robust stabilization are addressed, the present results are dependent on the size of delays and don't involve any tuning of parameters, as in the case with the reported results.6 For unknown statistics characteristics but limited power disturbance, the purpose is concerned with the problem of the robust H# filtering for a class of Lur'e singular system with state time-delays, parameters uncertainties, the sufficient condition is to design a robustly stable filter such that the uncertain Lur'e time-delay singular systems are not only regular... |