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

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)
Zbl 0569.93035
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