Nonlinear observer design by observer error linearization. (English) Zbl 0667.93014

Xia, Xiao-Hua; Gao, Wei-Bin

SIAM J. Control Optimization 27, No. 1, 199-216 (1989).

The paper discusses the following problem. Given a nonlinear control system \(\dot x=f(x,u)\), \(y=h(x)\), when does there exist a coordinate transformation \(z=\phi (x)\), such that in the new coordinates the system takens the form \(\dot z=Az+g(y,u)\), \(y=Cz\), where the appropriately dimensioned matrices A and C are in observer canonical form (or stated differently are in dual Brunovsky canonical form)? A solution to this problem admits the construction of an observer for the original dynamics, such that the error dynamics exponentially decays to zero as the solution of a stable linear differential equation. The paper identifies necessary and sufficient conditions for the solvability of this problem, thereby improving one of the results of an earlier paper [A. J. Krener and W. Respondek, SIAM J. Control Optimization 23, 197-216 (1985; Zbl 0569.93035)]. An explicit method for the computation of the desired coordinate transformation is given.

Reviewer: H.Nijmeijer

MSC:

93B07	Observability
93B17	Transformations
93C10	Nonlinear systems in control theory
93B10	Canonical structure
93B50	Synthesis problems
93C35	Multivariable systems, multidimensional control systems
93B40	Computational methods in systems theory (MSC2010)

Keywords:

linearization; nonlinear observers; nonlinear control system; coordinate transformation; dual Brunovsky canonical form

Citations:

Zbl 0569.93035