Robust Stability And Stabilization For Uncertain Time-delay Systems

Time delays are frequently encountered in various systems, such as industrial engineering systems, biological systems and social economics models. The stability and performance of such systems are often influenced seriously by the time delay. Therefore, the study of time-delay systems has attracted a great deal of attention over the past decades by many researchers. On the other hand, the mathematical model for control system design is only an approximate description to the real plant owing to the complexity of controlled plant. So it is always impossible to obtain accurate mathematics model for the practical controlled plant. There exists some difference between the mathematical model and the real system. And the difference of which some measure is able to get usually can be described as the uncertainties in the model arguments. The objective of robust control theory is to design a control law such that the resultant closed-loop system is stable and satisfies some prescribed performance for all admissible uncertainties.Since delay-dependent criteria are less conservative than delay-independent ones, the robust stability and stabilization problem for some uncertain systems with time-invariant and time-variant delays is studied in this dissertation. On the basis of linear matrix inequality (LMI) technique, the method of descriptor system model transformation and the free-weighting matrix approach are employed to obtain delay-dependent criteria for the stability of the systems. For uncertain networked control systems, the problem of robust control for uncertain continuous linear time-delay systems based on Lyapunov theory and descriptor system model transformation method is studied. For singular systems, the problems of robust stabilization is studied based on free-weighting matrix approach. And for Lurie systems, by using a new Lyapunov-krasovskii functional which splits the whole delay interval into two subintervals and defines a different energy function on each subinterval, some new delay-dependent criteria are presented to guarantee the robust absolute stability for the systems.The main contents of this dissertation are outlined as follows,(1) The problem of robust stabilization for a class of linear and nonlinear networked control systems with norm-bounded uncertain parameters is studied. Based on Lyapunov theory and descriptor system model transformation ap- proach, some sufficient conditions for the stabilization and state feedback control law are given in terms of LMI.(2) The problem of delay-dependent robust stabilization for norm-bounded uncertain continuous-time linear singular time-delay systems is investigated. By decomposing the nominal system into slow and fast subsystems, a delay-dependent condition is presented for the system to be regular, impulse free and stable, based on which, the robust stabilization problem is studied and the explicit expression for the corresponding state-feedback control law is given in terms of LMI. Compared with other methods, these criteria are easy to compute and less conservative than previous ones.(3) The problem of absolute stability and robust stability of a class of neutral Lurie direct control systems with mixed time-varying delays is investigated. By introducing the free-weighting matrix approach and s procedure, some delay-dependent criteria for absolute stability of the systems are gained. And the conditions are formulated by LMI which is easy to solve.(4) The problem of absolute stability and robust stability of a class of neutral Lurie indirect control systems with time delays is investigated. By using Jenson inequality and introducing some free-weighting matrices, some delay-dependent robust absolute stability criteria are presented in terms of strict linear matrix inequalities (LMIs).(5) The problem of robust absolute stability for a class of general Lurie systems with time delay is addressed. By using a new Lyapunov-krasovskii functional which splits the whole delay interval into two subintervals and defines a different energy function on each subinterval, some new delay-dependent criteria are presented and formulated by LMI.Finally, how the free-weighting matrix and new Lyapunov-krasovskii functional approach are used to get the delay-dependent robust stability and stabilization problem for networked control systems, singular systems and neutral Lurie control systems with delays is outlined. And the perspective of future studies is refered at the end of the dissertation.