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Explicit Necessary and Sufficient Conditions for Quadratic Linearization
Author(s) -
Ayalur Krishnamoorthy Parvathy,
Vijayarajan Kamaraj,
Devanathan Rajagopalan
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.499
Subject(s) - linearization , feedback linearization , mathematics , quadratic equation , constructive , affine transformation , polynomial , control theory (sociology) , transformation (genetics) , linear system , nonlinear system , control (management) , computer science , pure mathematics , mathematical analysis , process (computing) , biochemistry , chemistry , physics , geometry , quantum mechanics , artificial intelligence , gene , operating system
The existing necessary and sufficient conditions for quadratic linearization of control affine systems are in effect, constructive in nature. The exception is the classical result, which requires one to check involutive properties of distributions of the quadratic polynomials to be linearized. Nevertheless, the latter condition is difficult to verify. In this paper, we provide necessary and sufficient conditions for quadratic linearization that are not constructive but are based on checking a linear system of equations involving quadratic polynomial terms only. The system needs only to be put in controller normal form of the linear part which is known. Thus, the result is verifiable and explicit. Also, if required, once the quadratic linearization conditions are met, we show how to construct the coordinate and state feedback transformation to implement the linearization.