The contact problem for linear continuous-time dynamical systems: a system theoretical approach

The contact problem for linear continuous-time dynamical systems: a system theoretical approach

ten Dam, A.A.
Dwarshuis, E.
Willems, J.C.

National Aerospace Laboratory NLR

1995-06-28

In this paper linear time-invariant dynamical systems described by a combination of differential equalities and static inequalities in state-space formulation are investigated. Of special interest is the contact problem: the effect (of the boundary) of the constraint set on the behaviour of the system. This effect is studied by dividing the state-space in number of disjunct subsets. It is shown that these subsets are invariant under linear state feedback. Algoriüims are presented that calculate all these subsets in a finite number of steps. In our framework a specific place is reserved for modelling the laws of collision, i.e. physical modelling, which are regarded as external factors. Our main results are a system theoretical framework in which we describe what happens upon contact, and a precise definition of the constrained state-space system in terms of its restricted behaviour. The results presented here can be considered as an extension for restricted linear systems of the classic positive invariance theory for linear systems.

collsion modelling, constrained behaviours, contact problem, constrained linear systems, inequality constraints

http://resolver.tudelft.nl/uuid:70ec8319-b24e-4927-b6c4-fca1d83f0d5e

Nationaal Lucht- en Ruimtevaartlaboratorium

Campus only

NLR Technical Publication TP 95314 L

Aerospace Engineering Reports

report

(c)1995 National Aerospace Laboratory NLR