Sensitivity analysis and synthesis of multivariable systems

This paper consists of two main parts. The first part considers the sensitivity analysis of a linear time-invariant multivariable (multiple input-output) system represented by a system of first-order differential equations. Procedures which can be easily programmed on a digital computer are presented for the determination of: (1) the system transfer-function matrix; (2) sensitivity coefficients for the transfer-function matrix in terms of the system parameters. The second part contains a simple procedure for the synthesis of a linear single-variable (single input-output) system for specified characteristic roots. This is also shown to be a general procedure for the reduction of a system to (phase-variable) canonical form. The procedures of Part I and Part II are then applied to the synthesis of a single-variable system for insensitivity to parameter changes.