# zbMATH — the first resource for mathematics

A new method for linearizing non-linear systems: the pseudolinearization. (English) Zbl 0568.93007
Consider the single-input nonlinear system $$\dot x=f(x,u)$$. It has been shown that, under mild conditions, there exist transformations $$z=T(x)$$, $$v=S(x,u)$$ such that, in the z-space, the linear tangent model is independent of the operating point. A constructive procedure to obtain the above transformations is described. This new method is computationally attractive and effective in many practical cases.

##### MSC:
 93B17 Transformations 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations 37-XX Dynamical systems and ergodic theory
Full Text:
##### References:
 [1] CHAMPETIER , C. , REBOULET , C. , and MOUYON , P. , 1984 , submitted for the I.F.A.C. Congress , Budapest . [2] CLAUDE , D. , FLIESS , M. , and ISIDORI , A. , 1983 ,C.r. hebd. Séanc. Acad. Sci., Paris , 296 , 237 . [3] DE FORNEL , B. , HAPIOT , J. C. , REBOULET , C. , and BOIDIN , M. , 1980 ,Int. Conf. On Electrical Machines, Athens , pp. 793 – 800 . [4] HUNT L., Joint Automatic Control Conf. (1981) [5] HUNT L., Colloque CNRS (1982) [6] Su R., Syst. Control Lett. 2 pp 48– (1982) · Zbl 0482.93041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.