Abstract
This chapter studies stochastic stabilization of networked linear control systems over noiseless channels with finite capacity. Multi-dimensional systems within both fully observed and partially-observed settings are considered, and conditions for stochastic stabilizability are obtained. Using the state-dependent random-time drift criteria introduced in the previous chapter, stabilizing schemes are obtained under information rate constraint on the quantizers. The specifications considered in this chapter are the existence of an invariant probability measure and finiteness of certain moments.
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Andrews, G.E.: Number Theory. Dover, New York (1995)
Brockett, R., Liberzon, D.: Quantized feedback stabilization of linear systems. IEEE Trans. Autom. Control 45, 1279–1289 (2000)
Goodman, D.J., Gersho, A.: Theory of an adaptive quantizer. IEEE Trans. Commun. 22, 1037–1045 (1974)
Johnston, A., Yüksel, S.: Stochastic stabilization of partially observed and multi-sensor systems driven by Gaussian noise under fixed-rate information constraints. IEEE Trans. Autom. Control, under review (2013)
Kieffer, J.C., Dunham, J.G.: On a type of stochastic stability for a class of encoding schemes. IEEE Trans. Inf. Theor. 29, 793–797 (1983)
Liberzon, D., Nešić, D.: Input-to-state stabilization of linear systems with quantized state measurements. IEEE Trans. Autom. Control 52(5), 767–781 (2007)
Nair, G.N., Evans, R.J.: Stabilizability of stochastic linear systems with finite feedback data rates. SIAM J. Control Optim. 43, 413–436 (2004)
Yüksel, S.: Stochastic stabilization of noisy linear systems with fixed-rate limited feedback. IEEE Trans. Autom. Control 55, 2847–2853 (2010)
Yüksel, S.: A tutorial on quantizer design for networked control systems: Stabilization and optimization. Appl. Comput. Math. 11, 365–403 (2011)
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Yüksel, S., Başar, T. (2013). Stochastic Stabilization Over Noiseless Channels. In: Stochastic Networked Control Systems. Systems & Control: Foundations & Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7085-4_7
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DOI: https://doi.org/10.1007/978-1-4614-7085-4_7
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Publisher Name: Birkhäuser, New York, NY
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