Abstract
In this chapter, we deal with some finite-time control problems for discrete-time linear time-varying (DT-LTV) systems. First, we provide necessary and sufficient conditions for finite-time stability; such conditions can be regarded as the discrete-time counterparts of the results stated in Theorem 2.1. Indeed, one condition involves the computation of the state transition matrix; the other condition requires the solvability of a difference Lyapunov equality (DLE) or the feasibility of a difference linear matrix inequality (DLMI), respectively. The DLMI condition is the basis for the solution of the state and output feedback problems, which, again, are expressed in terms of optimization problems involving DLMIs.
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References
Amato, F., Ariola, M.: Finite-time control of discrete-time linear systems. IEEE Trans. Autom. Control 50, 724–729 (2005)
Amato, F., Carbone, M., Ariola, M., Cosentino, C.: Finite-time stability of discrete-time systems. In: Proc. American Control Conference, Boston, MA, pp. 1440–1444 (2004)
Amato, F., Ambrosino, R., Ariola, M., Calabrese, F.: Finite-time stability analysis of linear discrete-time systems via polyhedral Lyapunov functions. In: Proc. American Control Conference, Seattle, WA, pp. 1656–1660 (2008)
Amato, F., Ariola, M., Cosentino, C.: Finite-time control of discrete-time linear systems: analysis and design conditions. Automatica 46, 919–924 (2010)
Garcia, G., Tarbouriech, S., Bernussou, J.: Finite-time stabilization of linear time-varying continuous systems. IEEE Trans. Autom. Control 54, 364–369 (2009)
Packard, A., Balas, G., Safonov, M., Chiang, R., Gahinet, P., Nemirovski, A.: Robust Control Toolbox. The Mathworks, Natick (1984–2006)
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Amato, F., Ambrosino, R., Ariola, M., Cosentino, C., De Tommasi, G. (2014). FTS of Discrete-Time Linear Systems. In: Finite-Time Stability and Control. Lecture Notes in Control and Information Sciences, vol 453. Springer, London. https://doi.org/10.1007/978-1-4471-5664-2_5
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DOI: https://doi.org/10.1007/978-1-4471-5664-2_5
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5663-5
Online ISBN: 978-1-4471-5664-2
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