Abstract
We develop a method for the localization of spectra of multiparameter matrix pencils and matrix functions, which reduces the problem to the solution of linear matrix equations and inequalities. We formulate algebraic conditions for the stability of linear systems of differential, difference, and difference-differential equations.
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References
S. Boyd, L. El Chaoui, E. Feron, and V. Balakrishman, “Linear matrix inequalities in system and control theory,”Stud. Appl. Math.,15, 193 (1994).
A. G. Mazko, “Construction of analogs of the Lyapunov equation for a matrix polynomial,”Ukr. Mat. Zh.,47, No. 3, 337–343 (1995).
A. G. Mazko,Generalized Lyapunov Equation and Its Application to Problems of Stability and Localization of Spectra [in Russian], Author’s Abstract of the Doctoral Degree Thesis (Physics and Mathematics), Kiev (1995).
S. Gutman and F. Chojnowski, “Root-clustering criteria (II); Linear matrix equations,”IMA J. Math Contr. Inf.,6, 269–300 (1989).
A. G. Mazko, “Semiinversion and properties of matrix invariants,”Ukr. Mat. Zh.,40, No. 4, 525–528 (1988).
T. R. Crosslej and R. Porter, “Simple proof of the Simon-Mitter controllability theorem,”Electron Lett.,9, No. 3, 51–52 (1973).
E. N. Khasina, “On control over degenerate linear dynamical systems,”Avtom. Telemekh., No. 4, 30–37 (1982).
A. G. Mazko, “Distribution of roots of matrix polynomials with respect to two-dimensional curves,” in:Numerical-Analytic Methods for the Investigation of Dynamics and Stability of Complicated Systems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1984), pp. 90–96.
D.G. Korenevskii and A. G. Mazko, “Compact form of the algebraic criterion of absolute (with respect to delay) stability of solutions of linear difference-differential equations,”Ukr. Mat. Zh.,41, No. 2, 278–282 (1989).
A. L. Zelentsovskii, “Stability with probability one of solutions of systems of linear stochastic difference-differential equations,”Ukr. Mat Zh.,43, No. 2, 147–151 (1991).
D. Ya. Khusainov, “On a method for the construction of Lyapunov-Krasovskii functionals for linear systems with delay,”Ukr. Mat Zh.,41, No. 3, 382–387 (1989).
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Mazko, A.G. Localization of spectrum and stability of certain classes of dynamical systems. Ukr Math J 48, 1214–1221 (1996). https://doi.org/10.1007/BF02383867
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DOI: https://doi.org/10.1007/BF02383867