TY - GEN
T1 - The minimum achievable stability radius of switched linear systems with feedback
AU - Essick, Ray
AU - Philippe, Matthew
AU - Dullerud, Geir
AU - Jungers, Raphael M.
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/8
Y1 - 2015/2/8
N2 - We present a scheme for estimating the minimum achievable decay rate of a switched linear system via path-dependent feedback control, when the switching signal belongs to a language generated by a strongly connected graph. This growth rate is characterized by the constrained joint spectral radius (CJSR) of the system, a generalization of the joint spectral radius to account for the switching constraint. Our key tool in analyizing the CJSR is the multinorm, a collection of mode-indexed norms which demonstrate contractiveness along admissible modal trajectories. We may approximate the CJSR to any desired accuracy by computing quadratic multinorms as solutions to a system of LMIs, using an estimation scheme presented in [15]. These LMIs are of similar form to those which characterize the stability of the switched system in [6]. The feasiblity of any one of these LMIs allows the construction of a suitable controller; we use the infeasibility of such an LMI to provide a lower bound on the closed-loop decay rate achieved by any path-dependent controller.
AB - We present a scheme for estimating the minimum achievable decay rate of a switched linear system via path-dependent feedback control, when the switching signal belongs to a language generated by a strongly connected graph. This growth rate is characterized by the constrained joint spectral radius (CJSR) of the system, a generalization of the joint spectral radius to account for the switching constraint. Our key tool in analyizing the CJSR is the multinorm, a collection of mode-indexed norms which demonstrate contractiveness along admissible modal trajectories. We may approximate the CJSR to any desired accuracy by computing quadratic multinorms as solutions to a system of LMIs, using an estimation scheme presented in [15]. These LMIs are of similar form to those which characterize the stability of the switched system in [6]. The feasiblity of any one of these LMIs allows the construction of a suitable controller; we use the infeasibility of such an LMI to provide a lower bound on the closed-loop decay rate achieved by any path-dependent controller.
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U2 - 10.1109/CDC.2015.7402880
DO - 10.1109/CDC.2015.7402880
M3 - Conference contribution
AN - SCOPUS:84962019123
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4240
EP - 4245
BT - 54rd IEEE Conference on Decision and Control,CDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th IEEE Conference on Decision and Control, CDC 2015
Y2 - 15 December 2015 through 18 December 2015
ER -