TY - GEN
T1 - Stability analysis and stabilization of randomly switched systems
AU - Chatterjee, Debasish
AU - Liberzon, Daniel
PY - 2006
Y1 - 2006
N2 - This article is concerned with stability analysis and stabilization of randomly switched systems with control inputs. The switching signal is modeled as a jump stochastic process independent of the system state; it selects, at each instant of time, the active subsystem from a family of deterministic systems. Three different types of switching signals are considered: the first is a jump stochastic process that satisfies a statistically slow switching condition; the second and the third are jump stochastic processes with independent identically distributed values at jump times together with exponential and uniform holding times, respectively. For each of the three cases we first establish sufficient conditions for stochastic stability of the switched system when the subsystems do not possess control inputs; not every subsystem is required to be stable in the latter two cases. Thereafter we design feedback controllers when the subsystems are affine in control and are not all zeroinput stable, with the control space being general subsets of ℝm. Our analysis results and universal formulae for feedback stabilization of nonlinear systems for the corresponding control spaces constitute the primary tools for control design.
AB - This article is concerned with stability analysis and stabilization of randomly switched systems with control inputs. The switching signal is modeled as a jump stochastic process independent of the system state; it selects, at each instant of time, the active subsystem from a family of deterministic systems. Three different types of switching signals are considered: the first is a jump stochastic process that satisfies a statistically slow switching condition; the second and the third are jump stochastic processes with independent identically distributed values at jump times together with exponential and uniform holding times, respectively. For each of the three cases we first establish sufficient conditions for stochastic stability of the switched system when the subsystems do not possess control inputs; not every subsystem is required to be stable in the latter two cases. Thereafter we design feedback controllers when the subsystems are affine in control and are not all zeroinput stable, with the control space being general subsets of ℝm. Our analysis results and universal formulae for feedback stabilization of nonlinear systems for the corresponding control spaces constitute the primary tools for control design.
UR - http://www.scopus.com/inward/record.url?scp=39649122602&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=39649122602&partnerID=8YFLogxK
U2 - 10.1109/cdc.2006.377668
DO - 10.1109/cdc.2006.377668
M3 - Conference contribution
AN - SCOPUS:39649122602
SN - 1424401712
SN - 9781424401710
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2643
EP - 2648
BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 45th IEEE Conference on Decision and Control 2006, CDC
Y2 - 13 December 2006 through 15 December 2006
ER -