caa a22 4500 606166068 CHVBK 20210128100656.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10440-014-9956-2 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9956-2 Zero Dynamics and Stabilization for Analytic Linear Systems [Elektronische Daten] [Thomas Berger, Achim Ilchmann, Fabian Wirth] We combine different system theoretic concepts to solve the feedback stabilization problem for linear time-varying systems with real analytic coefficients. The algebraic concept of the skew polynomial ring with meromorphic coefficients and the geometric concept of (A,B)-invariant time-varying subspaces are invoked. They are exploited for a description of the zero dynamics and to derive the zero dynamics form. The latter is essential for stabilization by state feedback: the subsystem describing the zero dynamics are decoupled from the remaining system which is controllable and observable. The zero dynamics form requires an assumption close to autonomous zero dynamics; this in some sense resembles the Byrnes-Isidori form for systems with strict relative degree. Some aspects of the latter are also proved. Finally, using the zero dynamics form, we show for square systems with autonomous zero dynamics that there exists a linear state feedback such that the Lyapunov exponent of the closed-loop system equals the Lyapunov exponent of the zero dynamics; some boundedness conditions are required, too. If the zero dynamics are exponentially stable this implies that the system can be exponentially stabilized. These results are to some extent also new for time-invariant systems. Springer Science+Business Media Dordrecht, 2014 Time-varying linear systems nationallicence Feedback stabilization nationallicence Zero dynamics nationallicence Strict relative degree nationallicence Byrnes-Isidori form nationallicence Geometric control theory nationallicence Algebraic systems theory nationallicence Berger Thomas Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany aut Ilchmann Achim Institut für Mathematik, Technische Universität Ilmenau, Weimarer Straße 25, 98693, Ilmenau, Germany aut Wirth Fabian Dept. of Computer Science and Mathematics, University of Passau, 94030, Passau, Germany aut Acta Applicandae Mathematicae Springer Netherlands 138/1(2015-08-01), 17-57 0167-8019 138:1<17 2015 138 10440 https://doi.org/10.1007/s10440-014-9956-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9956-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Berger Thomas Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany aut NATIONALLICENCE 700 1- Ilchmann Achim Institut für Mathematik, Technische Universität Ilmenau, Weimarer Straße 25, 98693, Ilmenau, Germany aut NATIONALLICENCE 700 1- Wirth Fabian Dept. of Computer Science and Mathematics, University of Passau, 94030, Passau, Germany aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 138/1(2015-08-01), 17-57 0167-8019 138:1<17 2015 138 10440