Further Results on the Synthesis of FiniteTime Stable Systems

The logarithm of the square of the Euclidean norm is proposed as a Lyapunov function for synthesis of control systems which are finite-time stable. In some cases this appears to be a more useful Lyapunov function than the square of the Euclidean norm, since the inequalities resulting from use of a logarithmic Lyapunov function are typical of those which occur in classical stability theory. Thus, intuition developed in design of asymptotically stable systems is directly applicable to the design of finite-time stable systems. Also, in some cases the logarithmic Lyapunov function will provide a wider range of parameter values for which it is known that one has finite-time stability.