| In practice, no matter how accurately and carefully the engineer designs his circuit, the final product will contain imperfect elements which will cause the circuit performance to deviate from the anticipated response. One imperfection will be the inaccuracy of the element values. These values for the actual circuit can lie anywhere in a range, called tolerance range, which the designer declares acceptable for the purpose. The assignment of tolerance is, in fact, one of the most important parts of the circuit designer's task.;Worst-case tolerance analysis has been playing an important role in circuit design and manufacture stage.;Analog circuit testing at both the component and circuit levels is an essential tool for dealing with component variations due to manufacturing and production tolerances, aging, and environment. A computational approach is presented for computing the frequency-response of linear electrical circuits described by X&d2;=Ax+Bu where A is an interval matrix and whose parameters, in practice, usually deviate from their nominal values. As a result, the practical circuit responses will deviate from nominal responses too. Given tolerance ranges of circuit elements, the goal of worst case tolerance analysis is to compute the practical response ranges.;Differential equations of the linear circuits are derived, and the system matrices characterizing the state-space representation are obtained.;In this dissertation an algorithm was developed to obtain all possible vertex matrices for any size of given interval matrix and it was incorporated with Bhattacharyya and Keel algorithm for the determination of eigenvalue bounds for a family of interval matrices.;The problem treated in this dissertation is of considerable practical significance. Indeed, the circuit considered may be an amplifier or a control system (or part of it) and it is of paramount importance to know that the stability of the circuit (whatever its function) is guaranteed even in the presence of some uncertainties about the values of various component parameters. This problem usually is referred to as robust stability.;Illustrative examples are given to validate the method. |
