Abstract
The paper deals with discrete time-invariant systems with a delay in the control variable. The relations between different types of controllability and stabilizability are presented and discussed. The results are related to asymptotic null controllability, bounded feedback stabilizability and small feedback stabilizability for linear discrete-time systems with delay in control. The main tool employed is the technique of reducing the delayed equation to a delay-free equation. Thanks to this idea the criteria for bounded feedback stabilizability and small feedback stabilizability for the delayed systems are expressed in the appropriate properties of delay-free systems. Main results are analogical of this one proved in [18] for discrete time-invariant delay-free systems and to those from [14] for continuous-time systems. One of the additional result of this paper provides a criterion for controllability of discrete time system with delay in control. An important contribution of this paper is the indication of further generalizations of the obtained results.
The research presented here was done by authors as parts of the projects funded by the National Science Centre in Poland granted according to decision UMO-2017/27/B/ST6/00145 (JK), DEC-2017/25/B/ST7/02888 (AB) and Polish Ministry for Science and Higher Education funding for statutory activities 02/990/BK_19/0121 (AC).
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Babiarz, A., Czornik, A., Klamka, J. (2020). On Stabilizability of Discrete Time Systems with Delay in Control. In: Nguyen, N., Jearanaitanakij, K., Selamat, A., Trawiński, B., Chittayasothorn, S. (eds) Intelligent Information and Database Systems. ACIIDS 2020. Lecture Notes in Computer Science(), vol 12033. Springer, Cham. https://doi.org/10.1007/978-3-030-41964-6_16
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