BIlinear transformations between discrete- and continuouS- time infinite- dimensional linear systems
Ruth F. Curtain, Job C. Oostveen · NCSU Libraries Repository (North Carolina State University Libraries) · 1997
: We show that several system-theoretic properties are preserved under a bilinear transformation from a continuous-time linear system to a discrete-time one (and conversely) . For example, strong stability, infinite-time admissibility of the control and observation operators and approximate controllability and observability are all preserved. On the other hand, exponential stability (stabilizability) is not. Moreover, we establish a 1-1 correspondence between the solutions of the discrete- and continuous-time Lyapunov and Riccati equations. Key words: Bilinear transformations, Discrete-time infinite-dimensional linear systems, Continuous-time infinite-dimensional linear systems, Algebraic Riccati equation, Lyapunov equation, Spectral factorization. 1 Introduction There is a well-known bilinear mapping (Mobius transformation) that maps the open right-half plane C + = {s # C : #e(s) > 0} into the exterior of the unit disc D + = {z # C : |z| > 1}, and conversely, z = 1 + s ...