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Constrained Stabilization of Discrete-Time Systems

Balakrishnan, V. and Zheng, A. and Morari, M. (1994) Constrained Stabilization of Discrete-Time Systems. California Institute of Technology , Pasadena, CA. (Unpublished)

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Based on the growth rate of the set of states reachable with unit-energy inputs, we show that a discrete-time controllable linear system is globally controllable to the origin with constrained inputs if and only if all its eigenvalues lie in the closed unit disk. These results imply that the constrained Infinite-Horizon Model Predictive Control algorithm is globally stabilizing for a sufficiently large number of control moves if and only if the controlled system is controllable and all its eigenvalues lie in the closed unit disk. In the second part of the paper, we propose an implementable Model Predictive Control algorithm and show that with this scheme a discrete-time linear system with n poles on the unit disk (with any multiplicity) can be globally stabilized if the number of control moves is larger than n. For pure integrator systems, this condition is also necessary. Moreover, we show that global asymptotic stability is preserved for any asymptotically constant disturbance entering at the plant input.

Item Type:Report or Paper (Technical Report)
Additional Information:Submitted to International Journal of Robust and Nonlinear Control. Special issue on Control of Systems with Saturating Actuators. TECHNICAL MEMORANDUM NO. CIT-CDS 93-023. November 22, 1993; revised February 1994
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1993.023
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Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28041
Deposited By: Imported from CaltechCDSTR
Deposited On:19 Jul 2006
Last Modified:03 Oct 2019 03:28

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