H. Nicholson

Singular perturbational approximations for discrete-time balanced systems

A new zero-order singular perturbational type approximation is developed for model reduction of discrete-time linear systems. This approximation is also suitable for model reduction of systems which have fast subsystems and which are represented in the internally balanced format. Subsystem elimination as suggested by Moore for continuous-time systems does not generalize for the discrete-time case, and the singular perturbational approximation gives a particular solution to the discrete-time internally balanced model reduction problem.

Singular perturbational model reduction in the frequency domain

Singular perturbational approximations for linear continuous-time and discrete-time systems are developed in the frequency domain. It is shown that the familiar singular perturbational result is an approximation at the origin in the complex plane. However, if the system has multiple time-scale effects, other approximations can be obtained at different locations on the negative real axis to emphasize such behavior. The relationship between singular perturbational approximations and direct subsystem elimination is also investigated.

Minimality of SISO linear systems

A new test for minimality of single-input single-output state-space realizations is proposed based on rank conditions of a cross-Gramian type matrix without computing the controllability and observability Gramian matrices.

On the Cauchy index of linear systems

The Cauchy index for linear SISO systems is given by the signature of the cross-Gramian matrix W co defined by Fernando and Nicholson [1]. This index is useful in the qualitative understanding of systems, and the importance of this index in internally balanced model reduction is illustrated.