Decentralized Robust Control Theory And Its Application For Interconnected Uncertain Systems

This paper discusses decentralized robust control theory and its applications for large-scale interconnected systems. Beginning with the overview of the development and the present situation of decentralized robust control theory, the paper focuses on the decentralized state feedback and output feedback control for large-scale uncertain systems, decentralized passive control, decentralized H∞, control and decentralized output tracking control for large-scale system with time-delay, and the application to the process of zinc hydrometallurgy. The research consists of the following seven sections:Section 1 firstly proposes a design approach for decentralized H∞ control using state feedback for large-scale uncertain system based on the linear matrix inequalities(LMIs). And then, the studies come to decentralized reliable H∞ control problem when possible actuator failures occur within prespecified subset of actuators, and a design approach for the existence of a decentralized robust reliable H∞, controller is presented. After that, the decentralized H∞, control problem for a class of interconnected uncertain systems with time varying but norm-bounded parametric uncertainties is addressed and a sufficient condition which makes the closed-loop system decentralized asymptotically stable with disturbance attenuation is derived. Examples are given to demonstrate the effectiveness of the design approaches.Section 2 studies the decentralized robust H∞, observer-based control for a class of interconnected uncertain systems with time-varying uncertainties both in state and control matrices. A design method is derived for decentralized observer-based controller, which makes the closed-loop system quadratically stable with an H∞-norm bound for any admissible uncertainties. We obtain a design algorithm for decentralized observer-based controller on the basis of LMI conditions. Finally, a numerical example is given to demonstrate the design procedure for the decentralized Ho∞ observer-based feedback controller.Section 3 proposes a new parameterization approach to decentralized H∞ output feedback controller and a cross iterative algorithm for decentralized H∞ output feedback control design. By fixing some of the optimization variables of nonlinear matrix inequality, the decentralized output feedback problem can be converted to linear matrix inequality. Then the decentralized control problem turns to be some convex optimizations. The example shows the excellent convergence, directness and simplicity of computation, and convenience in application. Based on the research, the decentralized H∞ output feedback control is studied for large-scale systems with structured uncertainties. The uncertainty is assumed to be polytopic. With the strong robust H∞ performance criterion proposed, a sufficient condition and an iterative algorithm for theAbstractexistence of dynamic output feedback H controllers are given in terms of linear matrix inequalities. Also a given example shows the effectiveness of the algorithm.Section 4 studies the decentralied passive control of a class of large-scale systems with norm-bounded uncertainties by means of applying the notion of passivation to the decentralized control problem of large-scale systems and a sufficient condition for interconnected uncertain system to be asymptotically stable with strict passivity is given in terms of linear matrix inequality. A detailed simulation example is given to illustrate the theoretical developments.Section 5 proposes a decentralized H controller design approach for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. It is based on the existence of the solution to the LMI and the application of the Lyapunov stability theorem. The designed controller enables the closed-loop system decentralized asymptotically stable and satisfies the H performance attenuation.Section 6 discusses the decentralized robust tracking control problem for interconnected time-d...