H_∞Control And State Estimation Based On Variable Sampling Period

With the rapid development of digital technology, sampling control technology in which the control algorithm is implemented by computer has become a hot research topic in the field of automatic control. To cope with several negative factors such as network congestion, device failure, etc, the variable sampling technology has become the common scheduling strategy of network control. Therefore, it is of importance to analyze the effects of the variable sampling periods on system control design and state estimation in a quantitative manner and ensure the system to maintain good performance for a certain range of variable sampling periods. In the framework of time-dependent Lyapunov functional, the emphasis of this thesis is focused on the problem of sampled-data H∞control of linear uncertain singularly perturbed systems, the problem of sampled-data control for master-slave synchronization of chaotic Lur’e systems, and the design problem of sampled-data observers for Lipschitz nonlinear systems. The main work is as follows:1. The problem of robust sampled-data H∞control of linear uncertain singularly perturbed systems is investigated. The parameter uncertainties are assumed to be time-varying and norm-bounded. Two types of sampling mode are considered:multiple rate sampling, and fast rate sampling. By capturing the features of different types of sampling mode and the characteristics of two-time scale of the system under consideration, weighted time-dependent Lyapunov functionals are introduced to analyze the L2gain performance of the closed-loop system. New criteria for exponentially stability and finite L2gain are established. The new criteria reveal the relationship between L2gain, the singular perturbation parameter, and the upper bound of the sampling period. The new results are proved theoretically to be less conservative than the existing results. Moreover, linear matrix inequalities based solutions to ε-independent robust sampled-data H∞control problem are derived. An illustrative example is provided which substantiates the usefulness of the proposed method.2. The problem of sampled-data control for master-slave synchronization of chaotic Lur’e systems is studied. A new type of piecewise differentiable Lyapunov functionals is constructed in the framework of the input delay approach. The new Lyapunov functional is continuous at sampling times but not necessarily positive definite inside the sampling intervals. Compared with the existing works, the proposed method makes full use of the information on the piecewise constant input of the synchronization error system. Numerical simulation shows that the proposed method can significantly improve the upper bound of sampling period such that the master and the slave systems are synchronizied.3. The design problem of sampled-data observers for Lipschitz nonlinear systems with variable sampling period and sampling delays is investigated. By applying discontinuous Lyapunov functional based method, a new less conservative stability condition is derived to guarantee the global exponential stability of the estimation error system. The stability condtion is expressed in the form of linear matrix inequalities (LMIs). By solving a set of LMIs, the sampling observer gain matrix can easily be obtained. Finally, the effectiveness of the proposed method is illustrated through the flexible joint robotic arm and Chua’s circuit.