New results in subspace‐stabilization control theory

Source abstract

Subspace‐stabilization is a generalization of the classical idea of stabilizing motions of a dynamical system to an equilibrium state. The concept of subspace‐stabilization and a theory for designing subspace‐stabilizing control laws was introduced in a previously published paper. In the present paper, two new alternative methods for designing control laws that achieve subspace‐stabilization are presented. These two alternative design methods are based on: (i) a novel application of existing Linear Quadratic Regulator optimal‐control theory, and (ii) an algebraic method in which the control‐law is expressed as a linear feedback of certain “canonical variables.” In some cases, these new design methods may be more effective than existing ones. The results are illustrated by worked examples.