Multi-parameter sensitivity analysis of linear dynamic systems through the second method of Liapunov †

Abstract

Using the second method of Liapunov, a new procedure for performing sensitivity calculations in the stability analysis of linear dynamic systems is developed. Defining stability measure in terms of a Liapunov function and its time derivative, the paper formulates a method for the calculation of the sensitivity of stability measure to variations in system parameters. The method provides a basis for optimal stability design of linear dynamic systems, the criterion of optimality being that the sensitivity of the stability measure to parameter variations be zero. The feasibility and usefulness of the method are illustrated by numerical examples involving one and two variable parameters. Comparison of the time responses of the output variable obtained by using zero-sensitivity parameter settings with those resulting from the use of the minimum integral-square error criterion demonstrates the superiority of the proposed method. The procedure is simple and lends itself readily to programming on a digital computer.