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SUMMARY:Control theory of switches and clocks - Rodolphe Sepulchre\, Unive
 rsity of Cambridge
DTSTART:20180531T130000Z
DTEND:20180531T140000Z
UID:TALK106300@talks.cam.ac.uk
CONTACT:Alberto Padoan
DESCRIPTION:This talk will present a novel approach for the analysis and d
 esign of systems that switch and oscillate. While such nonlinear behaviors
  abound in control engineering of electrical\, mechanical\, and biological
  circuits\, it is often considered that they largely fall outside the scop
 e of control theory. In contrast\, the proposed approach closely mimics li
 near-quadratic dissipativity theory\, a very foundation of modern control 
 theory.\n\nIn its classical formulation\, dissipativity theory formulates 
 system properties as dissipation inequalities to be satisfied by the stora
 ge\, an abstraction of the system internal energy. Linear systems admit qu
 adratic storages. When the storage is positive definite\, it serves as a L
 yapunov function for stability analysis of equilibria. Our generalization 
 rests on two distinct ingredients. First\, we apply dissipativity theory d
 ifferentially: instead of studying the nonlinear system via the nonlinear 
 theory\, we apply the linear theory to a family of linearized systems. Sec
 ond\, we relax the positivity constraint of the quadratic storage to a fix
 ed inertia constraint. We allow for one negative eigenvalue in the analysi
 s of switches and two negative eigenvalues in the analysis of clocks.\n\nT
 he talk will illustrate the theory in classical models of switches and clo
 cks and discuss the potential of dissipativity theory for the analysis and
  design of interconnected systems away from equilibrium.
LOCATION:Cambridge University Engineering Department\, Lecture Room 5
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