Abstract
If a Lyapunov function is known for an asymptotically stable system of first order ordinary differential equations then it is shown in this paper how the known function may be used to construct new systems, based on the original one, which are also asymptotically stable. In other words, finite perturbations can be given to the original system which do not affect its stability behaviour. For constant linear systems this leads to a straightforward and hence potentially useful parametric procedure. It is also possible to construct an asymptotically stable linear system with a transient performance which can be largely predetermined. The connection with the method of linear bounds is discussed. Both the parametric perturbation and the synthesis procedures are generalised to include autonomous and non-autonomous non-linear systems. Some applications are given to systems with control.
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