TY - JOUR

T1 - Input/output-to-state stability and state-norm estimators for switched nonlinear systems

AU - Müller, Matthias A.

AU - Liberzon, Daniel

N1 - Funding Information: The work of M.A. Müller was supported by the Fulbright Commission and by the German Research Foundation (DFG) within the Priority Programme 1305 “Control Theory of Digitally Networked Dynamical Systems” and within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart. The work of D. Liberzon was supported by the NSF ECCS-0821153 grant and by a National Research Foundation Grant funded by the Korean Government ( NRF-2011-220-D00043 ). The material in this paper was partially presented at the 2010 American Control Conference (ACC’10), June 30–July 2, 2010, Baltimore, MD, USA and the 49th IEEE Conference on Decision and Control (CDC 2010), December 15–17, 2010, Atlanta, GA, USA. This paper was recommended for publication in revised form by Associate Editor Michael Malisoff under the direction of Editor Andrew R. Teel.

PY - 2012/9

Y1 - 2012/9

N2 - In this paper, the concepts of input/output-to-state stability (IOSS) and state-norm estimators are considered for switched nonlinear systems under average dwell-time switching signals. We show that when the average dwell-time is large enough, a switched system is IOSS if all of its constituent subsystems are IOSS. Moreover, under the same conditions, a non-switched state-norm estimator exists for the switched system. Furthermore, if some of the constituent subsystems are not IOSS, we show that still IOSS can be established for the switched system, if the activation time of the non-IOSS subsystems is not too big. Again, under the same conditions, a state-norm estimator exists for the switched system. However, in this case, the state-norm estimator is a switched system itself, consisting of two subsystems. We show that this state-norm estimator can be constructed such that its switching times are independent of the switching times of the switched system it is designed for.

AB - In this paper, the concepts of input/output-to-state stability (IOSS) and state-norm estimators are considered for switched nonlinear systems under average dwell-time switching signals. We show that when the average dwell-time is large enough, a switched system is IOSS if all of its constituent subsystems are IOSS. Moreover, under the same conditions, a non-switched state-norm estimator exists for the switched system. Furthermore, if some of the constituent subsystems are not IOSS, we show that still IOSS can be established for the switched system, if the activation time of the non-IOSS subsystems is not too big. Again, under the same conditions, a state-norm estimator exists for the switched system. However, in this case, the state-norm estimator is a switched system itself, consisting of two subsystems. We show that this state-norm estimator can be constructed such that its switching times are independent of the switching times of the switched system it is designed for.

KW - Input/output-to-state stability (IOSS)

KW - State-norm estimators

KW - Switched systems

UR - http://www.scopus.com/inward/record.url?scp=84865017134&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2012.06.026

DO - 10.1016/j.automatica.2012.06.026

M3 - Article

AN - SCOPUS:84865017134

VL - 48

SP - 2029

EP - 2039

JO - AUTOMATICA

JF - AUTOMATICA

SN - 0005-1098

IS - 9

ER -