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Complex Roots of a Polynomial, Linear Systems, Aperiodic Stability Analaysis, Modified Routh’s Table, Sign pair Criterion I and II

To evaluate the performance of a linear time-invariant system, various measures are available. In this paper employing Routh’s table, two geometrical criteria for the aperiodic stability analysis of linear time-invariant systems having real coefficients are formulated. The proposed algebraic stability criteria check whether the given linear system is aperiodically stable or not.The additional significance of the two criteria is , it can be used to count the number of complex roots of a system having real coefficients which is not possible by the use of original Routh’s Table. These procedures can also be used for the design of linear systems. In the proposed methods , the characteristic equation having real coefficients are first converted to complex coefficient equations using Romonov’s transformation. These complex coefficients are used in two different ways to form the Modified Routh’s tables for the two schemes named as Sign Pair Criterion I (SPC I) and Sign Pair Criterion II (SPC II). It is found that the proposed algorithms offer computational simplicity compared to other algebraic methods and is illustrated with suitable examples. The developed MATLAB program make the analysis most simple.