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Root-mean-square gains of switched linear systems: a variational approach. (English) Zbl 1153.93339
Summary: 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 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.

##### MSC:
 93B12 Variable structure systems 93C15 Control systems governed by ODE 93D20 Asymptotic stability of control systems 93C05 Linear control systems 49L20 Dynamic programming method (infinite-dimensional problems)
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