Optimization and Systems Theory Seminar
Friday, August 20, 1999, 11.00-12.00, Room 3721, Lindstedtsv. 25

Jorge Gonçalves
Laboratory for Information and Decision Systems
Massachusetts Institute of Technology
Cambridge, MA 02139-4307
E-mail: jmg@mit.edu

Global quadratic stability of limit cycles is common in relay feedback systems

For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global stability conditions, however, are practically non-existent. This paper presents conditions in the form of linear matrix inequalities (LMIs) that guarantee global asymptotic stability of a limit cycle induced by a relay with hysteresis in feedback with an LTI stable system. The analysis is based on finding global quadratic Lyapunov functions for a Poincaré maps associated with the RFS. We found that most Poincaré map induced by an LTI flow between two hyperplanes can be represented as a linear transformation analytically parametrized by a scalar function of the state. Moreover, level sets of this function are convex. The search for globally quadratic Lyapunov functions is then done by solving a set of LMIs. Most RFS analyzed by the authors were proven to be globally stable. Systems analyzed include minimum-phase systems, systems of relative degree larger than one, and of high dimension. This leads us to believe that quadratic stability of associated Poincaré maps is common in RFS.
Calendar of seminars
Last update: August 6, 1999 by Anders Forsgren, anders.forsgren@math.kth.se.