Rocha, Paula (Univ. of Aveiro)

Set-Controllability, Behavior Interconnection and Stabilization of Multidimensional Behaviors

Scheduled for presentation during the Mini-Symposium "Multidimensional systems: Algebraic and behavioral approaches" (ThA11), Thursday, July 27, 2006, 10:50−11:15, Room 104a

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 May 19, 2024

Abstract

As is well known, the central idea in the behavioral approach to control is the one of interconnection. This consists in the intersection of a given behavior to be controlled with a suitable controller-behavior, in order to obtain a desired (controlled) behavior. On the other hand, many relevant system properties, such as stabilizability, are defined in term of trajectory concatenation. Indeed, a 1D behavior B is said to be stabilizable if all its trajectories can be concatenated with trajectories that converge to zero; this definition can be generalized to the multidimensional case. Still at the level of trajectory concatenation, is the notion of set-controllability has been introduced: a behavior B is said to be set-controllable to a sub-behavior B* if its trajectories can be driven to B*in the sense that they can be concatenated with some trajectory in this sub-behavior. A natural question to pose is whether a stabilizable behavior is set controllable to a sub-behavior which is stable (in a sense to be made precise). The aim of this contribution is to study the relationship between the stabilizability of a multidimensional behavior B, its set-controllability to a stable behavior, and the possibility of stabilizing it by interconnection, i.e., of finding suitable controllers whose interconnection with B yields a stable behavior.