Lyapunov steepest descent control of constrained linear systems

A Lyapunov sufficiency condition is developed for steepest descent controls to yield global asymptotic stability of the origin in constrained linear systems. The results are applied to a previous counterexample for "optimal-aim" control. Using the more flexible Lyapunov steepest descent approach, global asymptotic stability is achieved, where optimal-aim control produced instability.