This thesis is concerned primarily with an investigation of the influence of eigenvectors and eigenvalues on linear system characteristics such as disturbance rejection and eigenvalue insensitivity to system parameter variations.

Existing design procedures for eigenvector/eigenvalue assignment are briefly reviewed and the results reinterpreted using range space restrictions. Such analysis readily shows that for a n^th order controllable system with r inputs, complete state feedback allows arbitrary assignment of n eigenvalues and up to r elements of each of the n eigenvectors.

The importance of eigenvectors in the design of control systens is illustrated by an investigation of the 'disturbability' characteristics of multivariable systems. A linear system is defined as 'undisturbable' with respect to a particular input variable if the state or output variables of interest are not disturbed by arbitrary variations in that input. Undisturbability is closely related to the system properties of uncontrollability and structural uncontrollability, but is not identical. Necessary and sufficient conditions for k ≤ r state variables to be undisturbable with respect to the j^th disturbance, require that the system matrix (or equivalently the matrix of eigenvectors) be quasi-triangular with a k×n-k offdiagonal partition of zero elements and that the corresponding k elements of the j^th column of the input distyrbance matrix be zero. These results together with existing eigenvector/eigenvalue assignment techniques provide a simple, straightforward design procedure to produce undisturbability in linear systems. The problem of asymptotic setpoint tracking in closed-loop undisturbable systems was also considered and it is shown that a solution to this problem is almost always possible.

Feedback and feedforward controllers designed to produce undisturbability were evaluated by experimental application to a computer controlled, pilot-plant evaporator. The results were superior to conventional multiloop controllers, and comparable to controllers designed using optimal quadratic techniques. The design method was also applied to 11^th and 20^th order models of two different binary distillation columns and evaluated by digital simulation.

For the class of systems which do not satisfy the necessary and sufficient conditions for undisturbability, a design procedure is proposed that uses state feedback control to:​ (i) minimise the effect of external disturbances on system outputs of interest and (ii) carry out arbitrary eigenvale eigenvalve assignment in the closed-loop system. An exper imental evaluation of this procedure on the pilot-plant evaporator demonstrated the practicality of this approach. Using duality this procedure is also appied to the design of full order observers to minimise the effect of unmeasurable external disturbances on the state estimate of interest.

A set of simple, constructive conditions for achieving eiqenvalue invariance to arbitrary variations in specified system parameters is derived in terms of the closed-loop system eigenvectors. An illustrative example demonstrates the superiority of this procedure over conventional pole placement techniques using unity-rank state feedback.