Free motion of sequence of similar aperiodic blocks

In the theory and practice of control systems design a model of the desired behavior which state matrix has the Newton's binary distribution of eigenvalues has found its widespread usage. Using the transfer functions apparatus in a structural representation of these systems yields systems in the form of a sequence of similar first order aperiodic blocks. The transient response of the system is characterized by the absence of overshoot. The situation changes considerably if the control system with a binomial distribution of eigenvalues is in a nonzero initial state. The system in the form of the sequence of similar first order aperiodic blocks mathematically turns out to be a three-parameter system with the following parameters: the absolute value of the negative real number, its multiplicity which is equal to the order of the system and the transfer coefficient. It was determined that in the three-parameter system, which is a present work research object, peaks of the state vector norm in the free motion trajectories may occur for any values of the absolute value of the negative eigenvalue.