A first analysis of stability when a constraint on the system state is encountered

The author considers a nonlinear system at a quasistatically varying, stable equilibrium encountering a linear constraint on the system state and studies the consequent change in system stability. The author formulates the problem of a nonlinear vector field encountering a linear constraint and notes that the stability of the constrained system is usually determined by the stability of the constrained linearization of the system. Therefore he studies the stability of a linear system encountering a linear constraint and gives conditions on the constraint guaranteeing stability or a certain change in the degree of stability when the constraint is encountered. The objective is to study the stability of the constrained system directly from the stability of the system and the constraint without explicitly determining the constrained system. This allows analytic study of the process of encountering a constraint. An application to improving the voltage stability of an electric power system near voltage collapse by selectively locking tap-changing transformers is briefly discussed