Co‐ordinate transformation in back‐stepping design for a class of non‐linear systems | Zendy

Zhan Wei | Zendy; Wang Le Yi | Zendy

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Co‐ordinate transformation in back‐stepping design for a class of non‐linear systems

Author(s) -

Zhan Wei,

Wang Le Yi

Publication year - 1995

Publication title -

international journal of adaptive control and signal processing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.73

H-Index - 66

eISSN - 1099-1115

pISSN - 0890-6327

DOI - 10.1002/acs.4480090505

Subject(s) - mathematics , transformation (genetics) , linearization , linear system , parametric statistics , simple (philosophy) , invariant (physics) , ordinate , control theory (sociology) , linear map , class (philosophy) , lti system theory , mathematical analysis , nonlinear system , pure mathematics , computer science , control (management) , geometry , biochemistry , chemistry , physics , statistics , philosophy , epistemology , quantum mechanics , artificial intelligence , mathematical physics , gene

In this paper the problem of existence and construction of a co‐ordinate transformation is investigated for non‐linear systems appearing in feedback linearization and back‐stepping adaptive control problems. Conditions are derived to completely characterize the classes of non‐linear systems that are transformable to the simple triangular and parametric simple triangular forms via linear transformations. the conditions are shown to be invariant under linear co‐ordinate transformations and non‐linear feedback. For systems satisfying these conditions, the development of the co‐ordinate transformation is shown to be equivalent to that of their first‐order approximations and is straightforward.

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