ortega, romeo (supelec), Barabanov, Andrey (Saint Petersburg State University), Escobar, Gerardo (IPICyT)

On Ultimate Boundedness Around Non-Assignable Equilibria of Linear Time-Invariant Systems

Scheduled for presentation during the Regular Session "Stability I" (WeA13), Wednesday, July 26, 2006, 12:30−12:55, Room 101

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

In this note we investigate the following question: given a (finite dimensional) linear time--invariant system and a constant desired value for its output. Assume there is no assignable equilibrium point corresponding to the desired output. Does there exists a (possibly dynamic, nonlinear, time--varying) controller such that the output ultimately enters a prescribed neighborhood of its desired value preserving all internal signals bounded? Our main contribution is the establishment of necessary and sufficient conditions, given in terms of a (computable) bound on the ``size" of the neighborhood, for the solution of the problem. Interestingly, there is no connection between this problem and the more familiar concepts of controllability and observability. However, we also prove that if the system has ``non--assignable values" for the output then it is non minimum phase.