2.42 Response of Continuous-Time LTI Systems
Pc.iYÙ0'nial differential operators are important in analysis of continuous-time linear systeb•.s. if a system is specified by its block diagram, we can use polynomial differential operat0'8 to simplify derivation of the system input—output description. To specify the problem completely so that the unique solution y(t) can be obtained for a known time func.c ;en x(t) and the coefficients ai and bk, we must specify (1) the interval of time over zhieh a solution is desired and (2) a set of n initial conditions for y(t) and its first n ! derivatives. In many cases the time interval is defined by 0 < t < +00 and the set of conditions is