×

Global stabilization of nonlinear systems via hybrid implementation of dynamic continuous-time local controllers. (English) Zbl 1429.93297

Summary: Given a continuous-time system and a dynamic control law such that the closed-loop system satisfies standard Lyapunov conditions for local asymptotic stability, we propose a hybrid implementation of the continuous-time control law. We demonstrate that subject to certain “relaxed” conditions, the hybrid implementation yields global asymptotic stability properties. These conditions can be further specialized to yield local/regional asymptotic stability with an enlarged basin of attraction with respect to the original control law. Two illustrative numerical examples are provided to demonstrate the main results.

MSC:

93D20 Asymptotic stability in control theory
93C10 Nonlinear systems in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Calafiore, G. C.; Possieri, C., A variation on a random coordinate minimization method for constrained polynomial optimization, IEEE Control Systems Letter, 2, 3, 531-536 (2018)
[2] Chai, J.; Casau, P.; Sanfelice, R. G., Analysis and design of event-triggered control algorithms using hybrid systems tools, (56th IEEE conf. decis. control (2017), IEEE), 6057-6062
[3] Collins, G., Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition, Lecture Notes in Computer Science, 33, 134-183 (1975)
[4] Goebel, R.; Sanfelice, R. G.; Teel, A. R., Hybrid dynamical systems, IEEE Control Systems, 29, 2, 28-93 (2009) · Zbl 1395.93001
[5] Goebel, R.; Sanfelice, R. G.; Teel, A. R., Hybrid dynamical systems: modeling, stability, and robustness (2012), Princeton University Press · Zbl 1241.93002
[6] Isidori, A., Nonlinear control systems (2013), Springer · Zbl 0569.93034
[7] Menini, L.; Possieri, C.; Tornambe, A., Algebraic methods for multiobjective optimal design of control feedbacks for linear systems, IEEE Transactions on Automatic Control, 63, 12, 4188-4203 (2018) · Zbl 1423.93121
[8] Postoyan, R.; Tabuada, P.; Nesic, D.; Martinez, A. A., A framework for the event-triggered stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 60, 4, 982-996 (2015) · Zbl 1360.93567
[9] Rockafellar, R. T.; Wets, R. J.-B., Variational analysis (2009), Springer: Springer New York
[10] Seuret, A., & Prieur, C. 2011. Event-triggered sampling algorithms based on a Lyapunov function. In 50th IEEE conf. decis. control; Seuret, A., & Prieur, C. 2011. Event-triggered sampling algorithms based on a Lyapunov function. In 50th IEEE conf. decis. control
[11] Shtessel, Y.; Edwards, C.; Fridman, L.; Levant, A., Sliding mode control and observation (2014), Springer: Springer New York
[12] Sontag, E. D., A “universal” construction of Artstein’s theorem on nonlinear stabilization, Systems & Control Letters, 13, 2, 117-123 (1989) · Zbl 0684.93063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.