Two new properties of the companion canonic representation of a controllable singleinput linear time-invariant system and a modified Leverrier algorithm are used to generate efficiently all sensitivity .functions of the system state variables.
Summary--A method is developed to generate by one nth order sensitivity model all the sensitivity functions [(OxO/(Oqj)]lqo, i= 1 ..... n, j= 1 ..... r for a single input, linear, time-invariant, controllable nth order system which depends on r different parameters. This represents an improvement over known methods for generating the sensitivity functions, which generally require a composite dynamic system of order n(r+l). In the development, two useful properties of the sensitiVity functions of the states of the companion form of a system, where the system A matrix is in companion form, are used. It is shown that all the sensitivity functions of the states of the companion form system can be generated by linear combinations of the signals on one sensitivity model of the system and the system states. The Leverrier algorithm has been extended so that the method of the paper is readily implemented on a digital or hybrid computer. Finally, an example is given, demonstrating how the technique of the paper can result in considerable time savings in the computer simulation and sensitivity analysis of systems.