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Linearized Oscillation Theory for a Nonlinear Nonautonomous Difference Equation Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

Authors : Artur Babiarz, Irina Banshchikova, Adam Czornik, Evgeniĭ Makarov, Michał Niezabitowski, Svetlana Popova

Published in: Difference Equations and Discrete Dynamical Systems with Applications

Publisher: Springer International Publishing

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Abstract

We discuss relations between the four formulations of the problem of assignability of the Lyapunov spectrum for discrete linear time-varying systems by a time-varying feedback. For two of them: global assignability and proportional local assignability, we have already [2‐4] obtained sufficient conditions in terms of uniform complete controllability and certain asymptotic properties of the free system. In the present paper we discuss the assumptions of our papers and demonstrate the use of the obtained conditions by numerical examples. We also compare our results with the classical pole placement problem. Finally, we formulate a couple of directions for further research in this area.

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previous chapter A Hilbert Space Approach to Fractional Difference Equations
next chapter Strongly Exponentially Separated Linear Difference Equations
Literature
1.
Antsaklis, P., Michel, A.: Linear Systems. Birkhauser, Boston (2005)
2.
Babiarz, A., Czornik, A., Makarov, E., Niezabitowski, M., Popova, S.: Pole placement theorem of discrete time-varying linear systems. SIAM J. Control Optim. 55(2), 671–692 (2017)MathSciNetCrossRef
3.
Babiarz, A., Banshchikova, I., Czornik, A., Makarov, E., Niezabitowski, M., Popova, S.: Necessary and sufficient conditions for assignability of the Lyapunov spectrum of discrete linear time-varying systems. IEEE Trans. Autom. Control 63(11), 3825–3837 (2018)MathSciNetCrossRef
4.
Babiarz, A., Banshchikova, I., Czornik, A., Makarov, E., Niezabitowski, M., Popova, S.: Proportional local assignability of Lyapunov spectrum of linear discrete time-varying systems. SIAM J. Control Optim., accepted for publication
5.
Banshchikova, I.N., Popova, S.N.: On the spectral set of a linear discrete system with stable Lyapunov exponents. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki 26(1), 15–26 (2016)CrossRef
6.
Barreira, L., Pesin, Y.B.: Lyapunov Exponents and Smooth Ergodic Theory. American Mathematical Society, vol. 23 (2002)
7.
Dickinson, B.: On the fundamental theorem of linear state variable feedback. IEEE Trans. Autom. Control 19(5), 577–579 (1974)MathSciNetCrossRef
8.
Elaydi, S.N.: An Introduction to Difference Equations. Springer, New York (2005)MATH
9.
Gaishun, I.: Discrete-Time Systems. Natsionalnaya Akademiya Nauk Belarusi, Institut Matematiki, Minsk (2001)MATH
10.
Halanay, A., Ionescu, V.: Time-Varying Discrete Linear Systems: Input-Output Operators, Riccati Equations, Disturbance Attenuation. Springer, Berlin (1994)CrossRef
11.
Johnson, R., Obaya, R., Novo, S., Núñez, G., Fabbri, R.: Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control. Springer, Berlin (2016)
12.
Klamka, J.: Controllability of Dynamical Systems. Kluwer Academic Publishers, Dordrecht (1991)MATH
13.
Ludyk, G.: Stability of Time-variant Discrete-Time Systems. Springer Fachmedien Wiesbaden GmbH, Bremen (1985)CrossRef
14.
Makarov, E.K., Popova, S.N.: Controllability of Asymptotic Invariants of Time-Dependent Linear Systems. Belorusskaya nauka, Minsk (2012)
15.
Sell, G.R.: Topological Dynamics and Ordinary Differential Equations. Van Nostrand Reinhold Mathematical Studies (1971)
16.
Sell, G.R.: The Floquet problem for almost periodic linear differential equations. Ordinary and Partial Differential Equations, vol. 239–251. Springer, Berlin (1974)CrossRef
17.
Sontag, E.D.: Mathematical Control Theory: Deterministic Finite Dimensional Systems, vol. 6. Springer Science & Business Media (2013)
Metadata
Title
Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems
Authors
Artur Babiarz
Irina Banshchikova
Adam Czornik
Evgeniĭ Makarov
Michał Niezabitowski
Svetlana Popova
Copyright Year
2020
Book
Difference Equations and Discrete Dynamical Systems with Applications

Print ISBN: 978-3-030-35501-2

Electronic ISBN: 978-3-030-35502-9

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-35502-9_5

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