Robust H_∞ Control And Model Reduction For Singular Systems

This paper mainly deals with H_∞ control for linear time-invariant (LTI) system, order-reduced H_∞ control for uncertain descriptor systems, and model reduction of descriptor systems. First, a descriptor system approach (DSA) is used to transform the normal system to a descriptor-system-form model equivalently. Based on descriptor systems' theory, new necessary and sufficient conditions of H_∞ control and α—stability for LTI systems are obtained. Furthermore H_∞/α—stability control is considered based on these new LMI (linear matrix inequality) conditions. Compared with the conventional Lyapunov shaping paradigm (LSP), it is evident that DSA is less conservative than before. Two numerical examples involving the well-known benchmark system are illustrated to show the improvement of the proposed DSA.Secondly, order-reduced H_∞ control for uncertain descriptor systems is studied. Based on strict LMIs, new sufficient conditions for generalized quadratic stability and H_∞ control of uncertain descriptor system are given, which can be solved by LMI toolbox in MATLAB directly. A parameterized functional observer with reduced order is formulated by the explicit solution for Sylvester functions. Then the parameterized formulation of the observer is used to obtain the order-reduced H_∞ controller with the constraint of the H_∞ performance of the closed-loop system. An illustrative example illustrates that the algorithm in this paper is efficient and solvable.At last we improve the results on model reduction for descriptor systems via covariance approximation. Genetic algorithm (GAs) is used to optimize all the parameters in the global feasible space of the reduced model. Based on the covariance definition for descriptor systems, the improvement algorithm makes the error, between the original system and reduced system, be optimized in the global feasible set. An example is provided to depict the output responses of the original and reduced systems, which shows the improvement clearly.This paper is organized as follows. In Chapter 1, a brief introduction is given to show the background and research techniques for what is mainly studied and applied in this paper. In Chapter 2, H_∞ control for LTI systems with an α—stability constraint is presented. As a main result in this paper, a descriptor system approach is explored to analyze the LTI systems. A new LMI-based algorithm for H_∞/α—stability control stemming from DSA is less conservative than the conventional method stemming from LSP. In Chapter 3, order-reduced H_∞ control for uncertain descriptor systems is discussed based on a parameterized...