TY - JOUR

T1 - Root-mean-square gains of switched linear systems

T2 - A variational approach

AU - Margaliot, Michael

AU - Hespanha, João P.

PY - 2008/9

Y1 - 2008/9

N2 - We consider the problem of computing the root-mean-square (RMS) gain of switched linear systems. We develop a new approach which is based on an attempt to characterize the "worst-case" switching law (WCSL), that is, the switching law that yields the maximal possible gain. Our main result provides a sufficient condition guaranteeing that the WCSL can be characterized explicitly using the differential Riccati equations (DREs) corresponding to the linear subsystems. This condition automatically holds for first-order SISO systems, so we obtain a complete solution to the RMS gain problem in this case.

AB - We consider the problem of computing the root-mean-square (RMS) gain of switched linear systems. We develop a new approach which is based on an attempt to characterize the "worst-case" switching law (WCSL), that is, the switching law that yields the maximal possible gain. Our main result provides a sufficient condition guaranteeing that the WCSL can be characterized explicitly using the differential Riccati equations (DREs) corresponding to the linear subsystems. This condition automatically holds for first-order SISO systems, so we obtain a complete solution to the RMS gain problem in this case.

KW - Algebraic Riccati equation

KW - Bilinear control systems

KW - Differential Riccati equation

KW - Hamilton-Jacobi-Bellman equation

KW - Maximum principle

KW - Optimal control

KW - Switched and hybrid systems

UR - http://www.scopus.com/inward/record.url?scp=50049104728&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2008.01.026

DO - 10.1016/j.automatica.2008.01.026

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AN - SCOPUS:50049104728

VL - 44

SP - 2398

EP - 2402

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 9

ER -