Abstract
Sufficient conditions for the stability of linear-switched systems with dwell-time and polytopic-type parameter uncertainties are presented. A Lyapunov function, in quadratic form, which is nonincreasing at the switching instants is assigned to each subsystem. During the dwell time, this function varies piecewise linearly in time after switching occurs and it becomes time invariant afterward. This function leads to asymptotic stability conditions for the nominal set of the subsystems that can be readily extended to the case where these subsystems suffer from polytopic-type parameter uncertainties. The method proposed is then applied to stabilization via state feedback, both for the nominal and the uncertain cases.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Geromel, J., Colaneri, P.: Stability and stabilization of continuous-time switched linear systems. SIAM J. Control Optim. 45(5), 1915–1930 (2006)
Colaneri, P.: Dwell time analysis of deterministic and stochastic switched systems. Eur. J. Autom. Control 15, 228–249 (2009)
Boyarski, S., Shaked, U.: Time-convexity and time-gain-scheduling in finite-horizon robust \(H_\infty \)-control. In: Proceedings of the 48th CDC09, Shanghai, China (2009)
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequality in Systems and Control Theory. SIAM Frontier Series (1994)
Kocvara, M., Stingl, M.: PENBMI User’s Guide, (Version 2) (2005). www.penopt.com
Toh, K-C., Todd, M.J., Tutuncu, R.H..: A MATLAB software for semidefinite-quadratic-linear programming (2009). http://www.math.nus.edu.sg/~mattohkc/sdpt3.html
Grant, M., Boyd, S.: CVX, Matlab software for disciplined convex programming (web page and software). (2009). http://stanford.edu/~boyd/cvx
M. Grant and S. Boyd, Graph Implementations for Nonsmooth Convex Programs, Recent Advances in Learning and Control (a tribute to M. Vidyasagar), V. Blondel, S. Boyd, and H. Kimura, editors, pages 95-110. Lecture Notes in Control and Information Sciences, Springer (2008). http://stanford.edu/~boyd/graph_dcp.html
YALMIP: A toolbox for modeling and optimization in MATLAB. In: Lfberg, J. Proceedings of the CACSD Conference, Taipei, Taiwan (2004). http://control.ee.ethz.ch/~joloef/yalmip.php
Apkarian, P., Gahinet, P.: A convex characterization of gain-scheduled \(H_{\infty }\) conterollers. IEEE Trans. Automat. Control 40(5), 853–864 (1995)
de Oliveira, M.C., Skelton, R.E.: Stability test for constrained linear systems. In: Reza Moheimani, S.O. (ed.) Perspectives in Robust Control. Lecture Notes in Control and Information Sciences, vol. 268. Springer, London (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Gershon, E., Shaked, U. (2019). Robust Stability and Stabilization of Switched Systems with Dwell Time. In: Advances in H∞ Control Theory. Lecture Notes in Control and Information Sciences, vol 481. Springer, Cham. https://doi.org/10.1007/978-3-030-16008-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-16008-1_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-16007-4
Online ISBN: 978-3-030-16008-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)