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The technique of splitting operators in perturbation control theory

Michail M. Konstantinov, Petko Hr. Petkov, Nikolaĭ D. Hristov (2005)

Kybernetika

The paper presents the technique of splitting operators, intended for perturbation analysis of control problems involving unitary matrices. Combined with the technique of Lyapunov majorants and the application of the Banach or Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the general feedback synthesis problem, and the pole assignment...

Transformation of nonlinear state equations into the observer form: Necessary and sufficient conditions in terms of one-forms

Vadim Kaparin, Ülle Kotta (2015)

Kybernetika

Necessary and sufficient conditions are given for the existence of state and output transformations, that bring single-input single-output nonlinear state equations into the observer form. The conditions are formulated in terms of differential one-forms, associated with an input-output equation of the system. An algorithm for transformation of the state equations into the observer form is presented and illustrated by an example.

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