Some Conditions for Monotone Nondecreasing Step Response with the Fastest Rise Time

초록

This paper investigates some conditions which guarantee the fastest rise and settling time in the step response of LTI(linear time-invariant) systems. As one of main results, it has shown that any LTI stable system having the relative degree 1 and the smallest absolute value of zeros' production has the fastest step response among those systems with the same positive DC gain and same poles. Also, it is shown that the result which is proposed is same as the cheap control in LQ(Linear Quadratic) problem for SISO(single-input, single-output) systems.