When stability is guaranteed by the second method of Lyapunov, the system response may still be unsatisfactory in that it is highly oscillatory and/or takes an inordinately long time to settle down. For instance, a numerical iterative loop whose convergence was guaranteed by the second method, converged so slowly as to be quite useless in practice. This aspect is particularly important when the Lyapunov method is used as a design tool. The designer must ensure that a satisfactory rate of convergence is obtained.

Inspec keywords: control system synthesis; Lyapunov methods; stability; convergence of numerical methods; iterative methods

Other keywords: stability; numerical iterative loop; Lyapunov method; design tool

Subjects: Stability in control theory; Control system analysis and synthesis methods; Nonlinear control systems; Interpolation and function approximation (numerical analysis)