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- W39479505 abstract "This introductory chapter provides the necessary background on control systems that we need for the development of the entropy theory. In Sect. 1.1, we give the definition of a control system which is basically the one from Sontag’s book (Mathematical Control Theory. Deterministic Finite-Dimensional Systems, 2nd edn., vol. 6, 1998). We also introduce particular classes of (time-invariant) systems, namely topological, linear, and smooth systems. Section 1.2 introduces the subclass of smooth systems which our main focus is on, the class of smooth systems given by differential equations. The third section serves for the introduction of several useful control-theoretic notions. In Sect.1.4, we prove elementary properties of the control flow associated with a control-affine system. Moreover, we establish the notions of control and chain control sets, and we give the proofs for some elementary properties of these objects. Most of this material stems from the book of Colonius and Kliemann (The Dynamics of Control, 2000). Finally, in Sect. 1.5, the linearization of a smooth system given by differential equations along a fixed trajectory and related notions are studied." @default.
- W39479505 created "2016-06-24" @default.
- W39479505 creator A5059120486 @default.
- W39479505 date "2013-01-01" @default.
- W39479505 modified "2023-09-27" @default.
- W39479505 title "Basic Properties of Control Systems" @default.
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- W39479505 doi "https://doi.org/10.1007/978-3-319-01288-9_1" @default.
- W39479505 hasPublicationYear "2013" @default.
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