A system is linear if its governing equations are linear in the state variables. In that case the time functions giving the state variables are simply pro­portional to the magnitude of nonautonomous input functions of given shape when the initial conditions are zero, and to the initial conditions if there are no nonautonomous inputs. If the parameters of the system and of the environment are constants, then the system is time invariant. The simplest class of systems is that which has both these properties—linearity and time invariance—and these can be completely analyzed by the available methods of linear mathematics. We shall denote these as linearjinvariant systems. Departure from either of these conditions leads to mathematical problems for which there may be no general methods of solution apart from numerical computation.

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