Minimal set of generators of controllability space for singular linear dynamical systems

Due to the significant role played by singular systems in the form E ¿ x ( t ) = Ax ( t ) , on mathematical modeling of science and engineering problems; in the last years recent years its interest in the descriptive analysis of its structural and dynamic properties. However, much less effort has been devoted to studying the exact con- trollability by measuring the minimum set of controls needed to direct the entire system E ¿ x ( t ) = Ax ( t ) to any desired state. In this work, we focus the study on obtaining the set of all matrices B with a minimal number of columns, by making the singular system E ¿ x ( t ) = Ax ( t ) + Bu ( t ) controllable.Postprint (author's final draft

Minimal set of generators of controllability space for singular linear systems

In recent years, there has been increasing the interest in the descriptive analysis of singular (also called generalized) systems in the form $E \dot x(t) = Ax(t)$ because they play important roles in mathematical modelling problems permeating many aspects of daily life arising in a wide range of applications. Considerable advances have been obtained in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the exact controllability measuring the minimum set of controls that are needed to steer the whole system $E \dot x(t) = Ax(t)$ toward any desired state. In this paper, we focus the study on the obtention of the set of all $B$ making the system $E \dot x(t) = Ax(t)+Bu(t)$ controllable