多項式形非線形系に対する状態観測器

概要

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For an nth order continuous time polynomic nonlinear system with m independent available outputs described by using high order form vectors, an observer of order n-m which is itself a polynomic nonlinear system driven by the available outputs and inputs of the original system is presented.A method, by which the difference of two higher order form vectors is factorized by the difference of two lower order form vectors, is given, and the error equation is described as a linear time varying system by using this method. It is shown that the time-varying matrix contained in the equation can be separated into a constant matrix and a time-varying vector. Then, sufficient conditions for the global uniformly asymptotical stability of the state estimation error are derived by Lyapunov methods on the basis of this separation. The results are very practical stability criteria since the definiteness of the constant matrices and the boundedness of the input, output and state vectors only have to be checked.The observer is further improved by using the linear combination of outputs for the reconstruction of unknown states in order to be applied to larger systems.A numerical example is included to show the performance of this polynomic nonlinear observer.
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