Analysis and Synthesis of Nonlinear System Based on Multi-model Method

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In order to overcome the inconsistency between the linearity assumed in most design methods of control systems and the nonlinearity which is common in most plants to be controlled, we propose the new notion of multi-model systems. the stabilizability of multi-model systems is the main concern of this research.First, we regard the multi-model system as a collection of the discrete points in the continuum of systems described as a perturbation set around the nominal plant model. This enables us to utilize various techniques of robust stabilization. We have proposed a method of constructing a stabilizer of a multi-model system based on the positive solution of an algebraic Riccati equation. The stabilizability of multi-model systems can be represented as the positivity of the solution of the algebraic Riccati equation. The intuitive meaning of this condition is clear.The stabilizability of multi-model systems has also been considered from the viewpoint of pole assignment. It has been shown that the stabilization is reduced to solving a set of multi-linear inequalities. For multi-model systems of the second order, this multi-linear inequalities are reduced to linear ones, and we obtain a necessary and sufficient condition of the stabilizability of the second-order multi-model system.Since it turned out that the control of multi-model systems is closely related to robust stabilization, and robust stabilization is solved by H control strategy, it is important to develop H control theory. In this project, we have established a unified approach to H control problem based on the new notion of conjugation.