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Controller reduction via stable factorization and balancing. (English) Zbl 0604.93020
A procedure is given to simplify the controller obtained by the LQG method. It is based on a certain right coprime factorization \(K(s)=N(s)D^{-1}(s)\) of the optimal controller transfer function. Using a balancing technique by Moore the authors approximate the pair D(s), N(s) by a low-order pair \(D_ 1(s)\), \(N_ 1(s)\) so that \(\| N(j\omega)-N_ 1(j\omega)\|_{L^{\infty}}\), \(\| D(j\omega)-D_ 1(j\omega)\|_{L^{\infty}}\) are sufficiently small. It is shown that the approximation \(K_ 1(s)=N_ 1(s)D_ 1^{-1}(s)\) gives a good accuracy of the approximation of the closed-loop behavior. A numerical example for a SISO system of 8th order is described in details.
Reviewer: A.Pervozvanskij

MSC:
93B50 Synthesis problems
15A23 Factorization of matrices
65F35 Numerical computation of matrix norms, conditioning, scaling
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
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