Non-regular feedback linearization of nonlinear systems via a normal form algorithm

Authors:
Daizhan Cheng;Xiaoming Hu;Yuzhen Wang
Affiliations:
Institute of Systems Sciences, Chinese Academy of Sciences, Beijing 100080, PR China;Optimization and Systems Theory, Royal Institute of Technology, Stockholm, Sweden;School of Control Science & Engineering, Shandong University, Jinan 250061, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2004

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Abstract

In this paper, the problem of non-regular static state feedback linearization of affine nonlinear systems is considered. First of all, a new canonical form for non-regular feedback linear systems is proposed. Using this form, a recursive algorithm is presented, which yields a condition for single input linearization. Then the left semi-tensor product of matrices is introduced and several new properties are developed. Using the recursive framework and new matrix product, a formula is presented for normal form algorithm. Based on it, a set of conditions for single-input (approximate) linearizability is presented.