K. Ozcaldiran

On the regularizability of singular systems

The property of regularity of singular systems is not a feedback invariant. To correct this deficiency a new property of regularizability is defined and geometric tests are given for it in terms of system matrices. Regularizability is shown to be the natural extension of regularity, which is a condition on the homogeneous system, to controlled singular systems. Definitions of controllability and reachability are modified depending on regularizability rather than regularity. A brief comparison of proportional and proportional-plus-derivative feedback laws in the context of making the closed-loop system regular, regular and reachable, and regular and controllable is also given. Dynamical interpretations of these properties are also presented. >

Geometric structure and feedback in singular systems

The output-nulling (A, E, R(B))-invariant subspaces are defined for singular systems, rigorously justifying the name and demonstrating that special cases of these geometric objects are the familiar subspace of admissible conditions and the supremal (A, E, R(B))-invariant subspace. A novel singular-system-structure algorithm is used to compute them by numerically efficient means. Their importance for describing the possible closed-loop geometric structure in terms of the open-loop geometric structure is shown. An approach to spectrum assignment in singular systems that is based on a generalized Lyapunov equation is introduced. The equation is used to compute feedback gains to place poles and assign various closed-loop invariant subspaces while guaranteeing closed-loop regularity. >

Generalized reachability subspaces for singular systems

One of the most important concepts of the geometric theory for proper linear systems is that of the controllability subspaces of

On the eigenstructure assignment of singular systems

(A,B)

Geometric notes on descriptor systems

. In an attempt to extend this concept to singular systems, it became clear that the nonequivalence of reachability and controllability for singular systems makes it necessary to define both controllability and reachability subspaces of

On a Special Case of the Morgan problem

(E,A,B)

A structural result on static output feedback

as different, though naturally related, entities.A subspace

On observability of singular systems

{\bf R}

Large-scale dynamical interconnections of stochastic singular systems

(respectively,

Partial Disturbance Rejection with Internal Stability and

{\bf C}