Output function control in general state space systems containing the first derivative of the input vector

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Abstract
In this paper, linear control systems are considered whose state equation is of the form Edx/ dt = AX+ Bo u + B1 where A, B,o and and B1 constant matrices, while E is a square matrix that may be singular and time-varying. The problem to be solved is if the output of the system is a prescribed function of find inputs that generate the desired output. The results are readily applicable to ‘ output zeroing problems ’ for example to the calculation of the finite and infinite zeros and the corresponding Zero-directions of regular and singular time-invariant systems. The assumption that E may have time-varying elements makes the method developed in tho paper applicable to certain perturbation problems.