| For many systems, the classical notion of Lyapunov stability criteria for stability of an equilibrium point provides a readily-verifiable test for stability of the equilibrium point. However, for a certain class of systems which are directionally constrained, this classical test for stability, and the classical definition of stability itself, has no meaning. An example of a directionally constrained system is one which is monotonically increasing regardless of the input to the system. Such systems often arise in materials processing situations, such as the manufacture of thin-film solar cels.;Previous work by Teri Piatt in her Ph.D. work at the University of Colorado developed a notion of stability for directionally constrained systems. The work presented here develops a Lyapunov-style stability criterion using the theory developed by Dr. Piatt. Using the mathematical notions of cones and conic containment, one defines a suitable V(x) and V˙(x), satisfying constraints here presented, which then imply directed stability of an equilibrium point. |
