New results in subspace-stabilization control theory (Q5950070)

Summary: 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.