Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
Theory of Invariance and its Applications-X. Block Decoupling
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1988 Volume 1 Issue 3 Pages 108-116


In this paper, we study the block decoupling problem of nonlinear systems with Cω-Structures : x=f (x) +G (x) u, y=h (x). Inputs and outputs are divided into N blocks, respectively. First, we propose a new algorithm by which we can determine the maximal locally controlled invariant distribution contained in Ker dh. This algorithm is an extension of nonlinear structure algorithm extensively used in the input-output linearlization, and can be applied to systems which is not input-output linearlizable. Moreover, it has an advantage in that we need not integrate the distribution.
Application of this algorithm to I-th output block yields a vector valued function zI(x).Then, the block decoupling problem is solvable if and only if each row of D(G)zI(x) is zero vector or is linearly independent of rows of other D(G)zJ(x)(J=1, …, N; IJ). The state feedback control law which accomplishes the block decoupling is derived from zI(x).

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