THE METHOD OF SPLITTING OPERATORS AND LYAPUNOV MAJORANTS IN PERTURBATION LINEAR ALGEBRA AND CONTROL

ABSTRACT In this paper we give a survey of recent results as well as new results in perturbation linear algebra and control, based on the method of splitting operators and Lyapunov majorant functions. Combined with the Schauder or Banach fixed point principles, this method allows to obtain rigorous non-local perturbation bounds for a set of important objects in linear algebra and control theory. Among them are the Schur system of a matrix, the QR decomposition of a matrix, the orthogonal canonical forms of a time-invariant linear system, the state and output feedback gains in pole assignment synthesis, the generalized Schur system of a pair of matrices, the polar decomposition of a matrix, the Hamiltonian Schur and Hamiltonian block-Schur forms of Hamiltonian matrices, and others. We also consider some other issues such as perturbation analysis of problems with non-unique solution and construction of improved asymptotic perturbation bounds. An important technique of the method considered is the constructi...

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