Abstract
This chapter discusses sensitivity operators for linear time-varying systems. A major problem in analysis and design of dynamical systems is the influence of parameter variations on system performance. It is customary to use feedback to counteract the affects of parameter variations. Although feedback can lead to an improvement in steady state accuracy, it is known that for single-input, single-output linear time-invariant systems, the effects of parameter variations on the system frequency response may be greater for the feedback system than for an open loop system with the same nominal transfer function. However, the feedback structure can be designed to be less sensitive to parameter variations than an open loop structure. This can be carried out by incorporating sensitivity functions in the design procedure. Sensitivity matrices have also been used to develop criteria for comparing feedback and open loop performances for multi-input, multi-output linear time-invariant systems. The chapter presents a direct comparison of open and closed loop errors via the sensitivity operator.
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