Practical Stabilization of Switched Affine Systems under Dwell Time: From Polytopic to p-Norm Lyapunov Functions
Abstract
This paper addresses the stabilization of switched affine systems under dwell-time constraints around a desired operating point that is not a common equilibrium of the subsystems. Since asymptotic stabilization is generally unattainable in this setting, the objective is to ensure that trajectories converge to and remain within a prescribed region containing the desired operating point. The main contribution is the development of Lyapunov-based tools that accommodate target regions more general than those induced by quadratic Lyapunov functions. In particular, we establish a constructive Lyapunov characterization for a broad family of weighted p-norm functions, which generalizes the classical quadratic Lyapunov equivalence and underpins the proposed hybrid-control and dwell-time developments. Focusing on the case in which the desired region is a polytope, and building on existing Lyapunov-based methods, we develop a constructive two-step method that starts from a polytopic Lyapunov certificate for the average system and yields a smooth weighted p-norm Lyapunov function for all sufficiently large p. We prove that this extension guarantees practical asymptotic stability of the desired operating point and yields a Lyapunov-certified invariant region under minimum dwell-time switching. Numerical examples illustrate the effectiveness of the proposed method.
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BibTeX
@misc{cinto2026practical,
title = {{Practical Stabilization of Switched Affine Systems under Dwell Time: From Polytopic to p-Norm Lyapunov Functions}},
author = {Felipe Cinto and Alexis J. Vallarella and Hernan Haimovich and Paulo C. Pellanda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37840},
eprint = {2609.37840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37840},
}
RIS
TY - UNPB
TI - Practical Stabilization of Switched Affine Systems under Dwell Time: From Polytopic to p-Norm Lyapunov Functions
AU - Felipe Cinto
AU - Alexis J. Vallarella
AU - Hernan Haimovich
AU - Paulo C. Pellanda
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37840
UR - https://arxiv.org/abs/2609.37840
AB - This paper addresses the stabilization of switched affine systems under dwell-time constraints around a desired operating point that is not a common equilibrium of the subsystems. Since asymptotic stabilization is generally unattainable in this setting, the objective is to ensure that trajectories converge to and remain within a prescribed region containing the desired operating point. The main contribution is the development of Lyapunov-based tools that accommodate target regions more general than those induced by quadratic Lyapunov functions. In particular, we establish a constructive Lyapunov characterization for a broad family of weighted p-norm functions, which generalizes the classical quadratic Lyapunov equivalence and underpins the proposed hybrid-control and dwell-time developments. Focusing on the case in which the desired region is a polytope, and building on existing Lyapunov-based methods, we develop a constructive two-step method that starts from a polytopic Lyapunov certificate for the average system and yields a smooth weighted p-norm Lyapunov function for all sufficiently large p. We prove that this extension guarantees practical asymptotic stability of the desired operating point and yields a Lyapunov-certified invariant region under minimum dwell-time switching. Numerical examples illustrate the effectiveness of the proposed method.
ER -