Research On Several Problems In The Control Of Time-delay Systems

In the practical control process, there existes the delay phenomenon widely due to the retardation characteristics of the system or external causes delay. Time-delay usually causes the control system performance degradation or even instability. The time-delay systems can usually be described as a retarded functional differential system. The existence of time-delay turns the closed-loop characteristic equation into a transcendental equation, resulting in stability analysis and controller design for systems difficult. At present, the methods based on frequency domain are mainly used in time-invariant delay systems, in which the necessary and sufficient stability criterion of the system can be obtained with complex solution. The methods based on the time domain can be provided stability analysis by constructing Lyapunov functional and selecting the inequality enlarged skill appropriately. This kind of methods can be convenient to study the time-varying delay systems, however the conservation is always exciting in these methods.The main contents of this dissertation are outlined as follows:1. For linear time-invariant delay systems, through a bi-vector transform method for solving the transcendental characteristic equation of time-delay systems, the distribution of the characteristic roots on the imaginary axis or the specified location on the left half-plane of the complex plane can be obtained, so that the stability criterion of the time-delay systems can be derived. From the amplitude and phase frequency characteristics, separating the delay value with the other parameters of the system explicitly, the critical stability time-delay can be made without conservative. On this basis, combining with interior point optimal method, a state feedback controller design is presented.2. For the interval time-varying delay systems and uncertain stochastic systems, by constructing Lyapunov-Krasovskii functional using non-uniform time-delay decomposition, we obtain a less conservative LMI-based robust asymptotic stability condition. Based on the obtained asymptotic stability criteria, this thesis further investigates the state feedback stabilization controller designed for the nominal systems and uncertain stochastic systems by the parameterization method.3. For the state observe problem of the interval time-varying delay systems and parameter uncertain stochastic systems with interval time-varying delay, by constructing Lyapunov-Krasovskii functional using non-uniform time-delay decomposition, a less conservatives H∞filter and L2-L∞filter are given based on LMI. Compared to the existing method, the designed filter in this thesis can obtain better filtering performance within the same maximum allowed delay.4. The stability analysis problem is considered for non-uniform sampling-data systems. In the case of known sampling interval and its distribution probability, the sampling-data system is transformed into an impulse model with multiple input delays. By constructing an appropriate discontinuous Lyapunov functional, a LMl-based global mean-square asymptotical stability criterion is derived with the free weight matrix approach. On this basis, studying the problem of fault estimation for a class of non-uniformly sampled-data systems, a novel augmented fault estimation observer design method is proposed to guarantee the exponential convergence of the estimation errors. Lastly, for state feedback stochastic stabilization of sampled-data control system with non-uniform sampling, a stochastic stabilization controller is given by using regulatory factor technique and cone complementary linearization method.