Lyapunov analysis of semistability

Semistability is the property whereby the solutions of a system converge to stable equilibrium points determined by the initial conditions. Important applications of this notion of stability include lateral aircraft dynamics and the dynamics of chemical reactions. A notion central to semistability theory is that of convergence in which every solution converges to a limit point that may depend upon the initial condition. We give sufficient conditions for convergence and semistability of nonlinear systems. By way of illustration, we apply these results to study the semistability of linear systems and some nonlinear systems.