Robust Control And Filtering For Singular Piecewise-affine Systems With Norm-bounded Uncertainties

Automatic control theory comes with the development of modern industry, the complexity and diversity of control system show a gradual upward trend in practical industrial applications. Therefore, the mehod of implementation more accurate control and grasp to the complex hybrid systems is one of the important subjects in the field of automatic control areas that we need to face. Among them, a class of hybrid systems always come with norm-bounded parameters is more common in practical application, the commonly used mehod of describing their is using a number of constant linear submodel within one system, and convex polyhedral domains which need to come with one-to-one correspondence. In this paper, singular piecewise-affine system with norm-bounded uncertainty parameters is one important mathematical model, which is belong to this class. Because of the characteristic of this kind of systems, this kind of systems are similar to the nonlinear system with infinite approximation characteristics. The system structure is completely similar to the hybrid system. Each subsystem can be seen as linear or affine in the area of effect. This makes the existing linear system theory can be used as an extension to explore the nature of the whole system. It is for this reason that we can combine traditional mathematical modeling method and new approaches in Electronic Science and Technology with automatic control theory, when we study piecewise-affine systems theory on generalized, which gives a lot of convenience to the theory research of generalized piecewise-affine system.In recent years, a lot of research on the basic theory of singular piecewise-affine systems have been done by domestic and foreign scholars, and some achievements have been made in engineering applications. Because of the singular piecewise-affine system is a kind of complex nonlinear system with non smooth and non continuous, on the other hand, it has a wide range of engineering background in the changeable real physical world and the specific application environment. Therefore, the theory and application of singular piecewise-affine systems are still the focus and hot spots in the field of automatic control. It also has a lot of difficult problems to be broken, which has important theoretical value and practical significance.On the basis of summarizing the previous studies, this paper studies the robust control and filter design problem for a class of singular piecewise-affine systems with norm-bounded parameter uncertainties. According to the different nature of feedback controller which is designed in this paper, the paper can be roughly divided into two parts:(1) design of feedback controller in general form, it is embodied in the second, third, fouth, fifth chapters, including the system robust stability, input saturation and state constrained system under the condition of generalized robust control for piecewise-affine systems, guaranteed cost control and H-infinity model predictive control of time-delay singular piecewise-affine systems;(2) elastic feedback controller design, it is embodied in the sixth chapter, including the problem of elastic controller stability for continuous singular piecewise-affine systems and H-infinity filter design for singular piecewise-affine systems. The main work of the paper can be reflected as follow:First of all, we consider the analysis problem with robust stability of singular piecewise-affine systems with norm-bounded parameters uncertainties. By choosing appropriate piecewise-affine Lyapunov function, we construct Lyapunov equation guaranteeing the singular piecewise-affine system is admissible and certain robust performance index can be given, the sufficient conditions for robust stability of the closed-loop system is obtained by using some basic lemmas and common methods of dealing with linear matrix inequalities. Based on the theory, LMIs solution of the existence of robust controller is given. Finally, we get the feedback controller gain to satisfy the robust control law of the singular piecewise-affine system. Eliminate the coupling relationship between the Lyapunov matrix and the system matrix in the process of solving the analysis problem. By using this method, conservative of the algorithm can be declined. The final results reflected the constraint of LMIs form, and we expect the more general results.Secondly, we study the robust control and guaranteed cost control problem of singular piecewise-affine systems with input saturation and system state constrained. Considering the singular piecewise-affine systems with input saturation and state constrained, LMIs solutions of guaranteed cost control with pole constraint are given, sufficient condition for the robust H-infinity stability of singular piecewise-affine systems is given. The method of designing output feedback controller are given by LMIs constraints, and the system state constrained embodiment is comprised a group of parameter LMIs conditions. Finally, the control performance of LMIs solution is given under limited conditions.Thirdly, we design the robust filter for singular piecewise-affine systems based on the previous robust stability analysis results and robust control law, non fragile robust filter LMIs solution is given. The state feedback controller is designed to form a closed loop system satisfy robust performance index of the non fragile robust filtering algorithm by a group of parameters LMIs, through carrying on the non fragile guaranteed control performance, ultimately, the system has enough room for adjustment to meet different performance requirements of the system, which is conducive to the state feedback control for system stabilization, and system fault diagnosis can be convenient ultimately.Then, we study the model predictive control and robust control problems for a class of singular piecewise-affine system with time-delay. By constructing a time-delay piecewise-affine Lyapunov-Krasovskii function, as so as combined with S-procedure lemma and several methods of processing the fundamental lemma of linear matrix inequality(LMI), model predictive control method of singular piecewise-affine systems is given based on introducing H-infinity state feedback controller. Ultimately, the states of closed-loop systems can be getten through the control input method to priori target states which are expected previously. For the robust H-infinity control problem of time-delay singular piecewise affine systems, we constructed a time-delay piecewise-affine Lyapunov-Krasovskii function, the method used before can be applicated. The final result can manifest the LMIs constraint form, the robust H-infinity control problem of singular piecewise-affine systems with time-delay is sloved.Finally, the resilient control stability poblem of continuous-time singular piecewise-affine system is discussed. We use a class of continuous-time singular piecewise-affine system with time-delay as a model to study the previous specified performance index and robust control performance. We construct the continuous-time singular piecewise-affine Lyapunov function, by using the S-procedure lemma and several basic processing method of disposing linear matrix inequality commonly used, non fragile guaranteed cost control method is proposed for the closed-loop system which can be satisfied the robust control index through state feedback controller. The feedback controller gain with H-infinity performance can be obtained by solving a set contains parameter LMIs, the non fragile guaranteed cost control system has been realized with sufficient room for adjustment to meet the different performance requirements of the system.