Abstract
The focus of this chapter is the stabilization of linear systems under saturating aperiodic sampled-data control. By employing a hybrid system representation, we establish conditions for the local and global stability of the origin of the closed-loop system using a specific class of quadratic timer (clock) dependent Lyapunov functions. These conditions are formulated as Sum-of-Squares constraints within optimization problems, enabling the design of stabilizing control laws that aim to maximize an estimate of the Region of Attraction to the Origin (RAO) or to maximize the admissible interval between two sampling instants in order to ensure that a certain given set of initial conditions is included in the RAO.
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Notes
- 1.
The level set \(\mathcal{E}_{P}^{x_p}\) corresponds to (9.9) in the case where \(V(\eta )=x'P(\tau )x\) and, since P can be normalized, \(\mu \) can be considered as 1 without loss of generality in this case.
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Acknowledgements
This work was supported in part by the “Agence Nationale de la Recherche” (ANR, France) under Grant HANDY ANR-18-CE40-0010, by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Brazil)-Finance Code 001, and by the Conselho Nacional de Desenvolvimento Cientfico e Tecnológico (CNPq, Brazil) - under Grant PQ-307449/2019-0.
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Fagundes, A.S., Gomes da Silva Jr., J.M., Jungers, M. (2024). Improved Synthesis of Saturating Sampled-Data Control Laws for Linear Plants. In: Postoyan, R., Frasca, P., Panteley, E., Zaccarian, L. (eds) Hybrid and Networked Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 493. Springer, Cham. https://doi.org/10.1007/978-3-031-49555-7_9
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