Extended Sensitivity Analysis and Stability Problems in Linear Systems

Abstract

In the theory of sensitivity analysis in control systems, sensitivity measure is usually defined as a type of differential coefficient. However, such a measure represents only a first-order approximation of the quantity under interest corresponding to “small” parameter (or system) variation. The extent of the variations within which the measure is valid is not clearly defined: in addition, it is not much effective for the case of time-varying parameter.
In this paper each variable of generalized linear systems is investigated in “normed space” and sensitivity measure is defined as norm of linear operator (sensitivity operator). Therefore, the influence of parameter variations is quantitatively evaluated and the sensitivity analysis of linear systems including the case of time-varying parameter is discussed at large. That is also investigated in some definite spaces. When the sensitivity measure is bounded, the perturbed system is stable. Hence, several conditions for the stability of perturbed linear systems are derived. Finally the case of frozen parameter (or slowly varying parameter) is discussed in detail.