TY - JOUR
T1 - Windows of opportunity for the stability of jump linear systems
T2 - Almost sure versus moment convergence
AU - Porfiri, Maurizio
AU - Jeter, Russell
AU - Belykh, Igor
N1 - Funding Information:
Dr. Maurizio Porfiri is a Professor in the Department of Mechanical and Aerospace Engineering at New York University Tandon School of Engineering. He received M.Sc. and Ph.D. degrees in Engineering Mechanics from Virginia Tech, in 2000 and 2006; a “Laurea” in Electrical Engineering (with honors) and a Ph.D. in Theoretical and Applied Mechanics from the University of Rome La Sapienza” and the University of Toulon (dual degree program), in 2001 and 2005, respectively. He is engaged in conducting and supervising research on dynamical systems theory, multiphysics modeling, and underwater robotics. Maurizio Porfiri is the author of more than 250 journal publications and the recipient of the National Science Foundation CAREER award. He has been included in the “Brilliant 10” list of Popular Science and his research featured in all the major media outlets, including CNN, NPR, Scientific American, and Discovery Channel. Other significant recognitions include invitations to the Frontiers of Engineering Symposium and the Japan–America Frontiers of Engineering Symposium organized by National Academy of Engineering; the Outstanding Young Alumnus award by the college of Engineering of Virginia Tech; the ASME Gary Anderson Early Achievement Award; the ASME DSCD Young Investigator Award; and the ASME C.D. Mote, Jr. Early Career Award.
Funding Information:
This work was supported by the US Army Research Office under Grant No. W911NF-15-1-0267 with Drs. Samuel C. Stanton and Alfredo Garcia as the program managers. Views expressed herein are those of authors, and not of the funding agency. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Oswaldo Luiz V. Costa under the direction of Editor Richard Middleton.
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2019/2
Y1 - 2019/2
N2 - In this paper, we examine the role of the switching period on the stochastic stability of jump linear systems. More specifically, we consider a jump linear system in which the state matrix switches every m time steps randomly within a finite set of realizations, without a memory of past switching instances. Through the computation of the Lyapunov exponents, we study δ-moment and almost sure stability of the system. For scalar systems, we demonstrate that almost sure stability is independent of m, while δ-moment stability can be modulated through the selection of the switching period. For higher-dimensional problems, we discover a richer influence of m on stochastic stability, quantified in an almost sure and a δ-moment sense. Through the detailed analysis of an archetypical two-dimensional problem, we illustrate the existence of disconnected windows of opportunity where the system is asymptotically stable. Outside of these windows, the system is unstable, even though it switches between two Schur-stable state matrices.
AB - In this paper, we examine the role of the switching period on the stochastic stability of jump linear systems. More specifically, we consider a jump linear system in which the state matrix switches every m time steps randomly within a finite set of realizations, without a memory of past switching instances. Through the computation of the Lyapunov exponents, we study δ-moment and almost sure stability of the system. For scalar systems, we demonstrate that almost sure stability is independent of m, while δ-moment stability can be modulated through the selection of the switching period. For higher-dimensional problems, we discover a richer influence of m on stochastic stability, quantified in an almost sure and a δ-moment sense. Through the detailed analysis of an archetypical two-dimensional problem, we illustrate the existence of disconnected windows of opportunity where the system is asymptotically stable. Outside of these windows, the system is unstable, even though it switches between two Schur-stable state matrices.
KW - Discrete-time
KW - Linear stochastic systems
KW - Lyapunov exponent
KW - Mean-square
KW - Stability
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U2 - 10.1016/j.automatica.2018.11.028
DO - 10.1016/j.automatica.2018.11.028
M3 - Article
AN - SCOPUS:85057828144
SN - 0005-1098
VL - 100
SP - 323
EP - 329
JO - Automatica
JF - Automatica
ER -