Abstract
We handle the concept of optimizability in the context of infinite-horizon discrete-time Linear-Quadratic optimal control systems. It is shown that this concept is equivalent to: 1) the existence of a positive semi-definite (PSD) solution of the Algebraic Riccati Equation (ARE), 2) optimizability using state feedback, and 3) output-stabilizability of the system, i.e. stabilizability of any observable part of the system. It is then found that the optimal minimal cost is defined by the minimal PSD-solution of the (ARE), which generates an optimal state feedback. The latter becomes stabilizing (i.e. the closed-loop state is bounded by a decreasing exponential) iff the system is output-stabilizable and detectable.
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© 1997 Springer Fachmedien Wiesbaden
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Callier, F.M. (1997). On Output-Stabilizability and Detectability of Discrete-Time LQ-Optimal Control Systems. In: Helmke, U., Prätzel-Wolters, D., Zerz, E. (eds) Operators, Systems and Linear Algebra. European Consortium for Mathematics in Industry. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-09823-2_5
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DOI: https://doi.org/10.1007/978-3-663-09823-2_5
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-663-09824-9
Online ISBN: 978-3-663-09823-2
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