Root-mean-square gains of switched linear systems: A variational approach

Michael Margaliot*, João P. Hespanha

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2398-2402
Number of pages5
Issue number9
StatePublished - Sep 2008


  • Algebraic Riccati equation
  • Bilinear control systems
  • Differential Riccati equation
  • Hamilton-Jacobi-Bellman equation
  • Maximum principle
  • Optimal control
  • Switched and hybrid systems


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