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A practical closed form solution for systems with variable eigenvalues via bilinear system theory
Author(s) -
Brandenbusch Wolfgang,
Stehle Werner
Publication year - 1981
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490090111
Subject(s) - eigenvalues and eigenvectors , mathematics , laplace transform , constant (computer programming) , matrix (chemical analysis) , variable (mathematics) , bilinear transform , bilinear form , invariant (physics) , lti system theory , transformation (genetics) , mathematical analysis , linear system , pure mathematics , computer science , physics , mathematical physics , quantum mechanics , digital filter , materials science , filter (signal processing) , composite material , computer vision , programming language , biochemistry , chemistry , gene
This paper treats systems in state variable formulation with non‐constant, parameter controlled system matrices. The synthesis of a system with controlled eigenvalues (ECS) is given. The synthesized system is a commutative bilinear system. Its solution has a closed form and is based on the solution of just one time invariant system although as many arbitrary time functions are involved as the system has independent states. The ECS is homologous to any system with a system matrix being an arbitrary, possibly time‐dependent function of a single constant system matrix. All results are deduced for multiple eigenvalues of the system matrix including single eigenvalues as a special case. They are fully analogous to the solution of time invariant systems by means of the Laplace transformation.