Delay-dependent Variable Structure Control For T-S Fuzzy Uncertain Time-Delay Systems

As is well known, there are some efficient control methods in practical applications, for example, variable structure control, adaptive control, fuzzy control, robust control etc. Variable structure control is a kind of nonlinear control approach, whose characteristic is that the structures of the feedback control law change according to the certain rule while the system state crosses the different region of the state spaces. And, the control system has the stronger adaptive ability to the factors which include internal parameter perturbations and external disturbances of the controlled plant. That is, the variable structure control system is insensitive to internal parameter perturbations and external disturbances on the sliding surface. In fact, uncertainties always appear in the controlled plants, such as parameter uncertainties, time-delay uncertainties, nonlinear perturbation, etc. Therefore, the problem of variable structure control for T-S fuzzy time-delay systems with uncertainties becomes more important in control community.The main results in the thesis are as follows:(1)The significance of variable structure control issue is introduced, both in theory and in applications. And the related development abroad and at home is retrospected briefly.(2)The problem of delay-dependent variable structure control for T-S fuzzy systems with constant or time-varying delays, parameter uncertainties and external disturbances is studied in this paper. The parameter uncertainties include two different cases: one is norm-bounded by linear constraints, the other satisfies matching conditions with uncertainties bounded by high-order nonlinear constraints. External disturbances satisfy matching conditions and are bounded by continuous functions. Various design methods and existent conditions of variable structure controllers are proposed in terms of LMIs for two different time-delay cases by using PDC technique, Lyapunov stability theory. The designed variable structure controllers could drive the trajectories of the closed loop system onto the so-called sliding surface in finite time and maintain on it thereafter, and on the sliding surface the system is insensitive to internal parameter perturbations and external disturbances. Accordingly, reduced system is asymptotically stable on sliding surface. The efficiency of our design method is finally verified by simulation on a continuous stirred tank control problem.(3) The main results of the thesis are concluded, and the issues of future investigation are proposed.