Bilinear Control Systems

A control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. The study of bilinear control systems began in the 1960s and has since developed into a fascinating field, vital for the solution of many challenging practical control problems. Its methods and applications cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control in quantum physics and the study of Lie semigroups. This book introduces and surveys bilinear control systems theory from a mathematical viewpoint. The exposition is at the first-year graduate level. Topics include an introduction to Lie algebras, matrix groups and semigroups; the controllability, stabilization, and observability of bilinear systems; nonlinear systems analytically equivalent to bilinear systems; series representations for input-outputmappings; and random inputs. To assist the reader there are exercises; Mathematica scripts; and appendices on matrix analysis, differentiable maps and manifolds, Lie algebra, and Lie groups.