The Research On Stability And Stabilization Of Large-scale Systems Based On Comparison Principle Theory

Comparison Principle Theory (CPT) approach has been widely applied for its unique deceasing dimensions of the complex systems and complicated degree of the analysis. It has become an important in analysis and design of the robust control. The doctoral dissertation focuses on the decentralized state feedback and output feedback robust control using CPT approaches. Some theorems of existing decentralized state and output feedback controllers for large scale nonlinear systems are proposed, while the algebraic algorithms are contracted also. The gain matrix designs are leaded to poles placements. As to the state feedback controller design, the decentralized controllers can be obtained directly if the performance indexes (decay rates) are provided, while as to the output feedback controllers, the decentralized controllers are not only based on the provided indexes but also on resolutions of the several LMI. The only assumption is that the uncertainties are norm bounded. This modification is nearly closed to practice. Our algorithm appears more valid to obtain small gain matrices. The main work and research results are summarized as follows:(1) The relationship between the stability of the interconnected systems and the eigenvalues of the system matrix are developed. This remarkable improvement differs from the previous indirect relationship, which is direct.(2) The diversities between layers are considered. For the sake of getting more economic or effective controllers, a mapping law is proposed that the sub-systems in a space are mapped algebraic equally into another space to reduce differences by optimal theory. No any restrictions are added to the controlled systems, and without need to solve coupled Lyapunove or Riccati equalities. At same time the perform indexes are considered.(3)For the classes of nonlinear large-scale systems with Lipchitze conditions and large-scale delay systems, several conditions for decentralized stabilizing are founded using CPT. For state feedback controller design, an algorithm is developed accord to the given perform index (decay-rates). This method needs not select in advance parameters;if provided the required decay rates of the sub-systems, the expected gain matrix is obtained instantly.(4) For the two classes of large-scale systems mentioned above, some related theorems for output feedback controllers design are distributed. We firstly find out thecorresponding existing conditions of output feedback controllers whether a group of LMI equations are solved or not. An algorithm is constructed based on the resolutions of LMI equations. The method is convenient to calculation, evaluation and application.(5) Two applications of decentralized robust stabilization control are studied for PUMA562 robot and pendulum GM400. Based on the problem of robust stability, poles placement method is applied to get the desired decentralized robust controllers, and two classes of control systems for 4th and 5th joints of PUMA562 and pendulum400 are used to test validness of the proposed approaches.The simulations and practical results show that the theoretical research is valid and reliable. The control scheme appears feasible. A new design approach has been offered to robust control.