A GENERAL ORTHOGONAL POLYNOMIAL APPROACH TO THE SENSITIVITY ANALYSIS OF LINEAR-SYSTEMS

A new computational approach for the sensitivity analysis of linear systems is proposed. In this approach, the state variables are approximated using a set of orthogonal functions that need not satisfy the initial conditions a priori. An approach, similar to a variational virtual work approach with weighing functions, is used to convert the system state differential equations into a set of STate Algebraic Equations (STAEs) and a Lagrange multiplier technique is used to enforce the initial conditions. The STAEs are differentiated with respect to system parameters, which may vary, to obtain a set of SEnsitivity Algebraic Equations (SEAEs) thus eliminating the need for integrating the state and the sensitivity differential equations. The coefficient matrix in the SEAEs is the same as in the STAEs. Also, the coefficient sensitivity terms satisfy some properties. These facts are used to reduce the computational time. An example is solved using three different sets of orthogonal polynomials and the power series to demonstrate the feasibility and efficiency of this approach.