The transient behavior of autonomous nonlinear control systems

This paper shows a method to find domains of the phase space of an autonomous system, where the transient responses are faster than those produced by the linear system
\dot{y}=-\lambda y
. This system is considered as a standard; the domains are said to correspond to a restriction of quality equal to λ. The problem is transformed into one of finding relative stability domains for a special time-dependent Liapunov function. As an example, a second-order nonlinear servomechanism is studied. The objectives that can be called best estimates of domains or of restrictions of quality are too many; two of them are exemplified by means of a straightforward variational technique.