Long-run behavior of constrained discrete-time linear dynamical systems

We consider a system of linear equations whose variablesy(t) E^m describe an economy or process which is observed in succeeding discrete time periodst. With forms given for the equations relating the values of the state vectory(t) in succeeding periods and limiting the set of feasible choices ofy(t) in each period, conditions which determine the nature of feasible sequences of state vectors are given, and the characteristics ofy(t) ast are analyzed. Some of the results are studied in the framework of specified infinite horizon optimization problems.Research for this paper was partially supported by the Office of Naval Research, Contract N00014-69-A-0200-1055 at the Operations Research Center of the University of California, Berkeley.