Changing the State of a Linear System by use of Normal Function and its Derivatives†

Abstract

For a linear system with real poles, two problems have bean attacked 1. Achieving a desired state from ground state in minimum time 2. Achieving maximum distance from the origin (ground state) when the excitation is magnitude limited. As is known (Gupta l962, Zacleh 1900), the state of a system can be changed in zero time using the impulse-function and its derivatives. This is, of course, not practical and therefore in this paper the impulse function is approximated by normal function and the above problems are attacked using this normal function and its derivatives. This method shows to what degree the impulse function response can be approximated using this typo of excitation and shows the practicality of this type of input.