Linear System Theory

Abstract

Linear system theory is the central part of this book. It is developed for state-space models and centered right at the intrinsic structural properties of linear systems in relation to their inputs and outputs. This chapter examines basic issues such as realization, observation, and control. It studies system structures from inputs to state vectors and from state vectors to outputs via rigorous mathematical analysis. However it is the conceptual notions of reachability, observability, stabilizability, and detectability that are at the heart of the linear system theory and are the central theme of this chapter. These fundamental concepts empower not only our insight to minimal realization, but also to optimal estimation and control to be investigated in a later chapter. Moreover Lyapunov stability, i.e., asymptotic stability and linear feedback stabilization are developed based on these concepts. Both numerical tool and illustrative examples are presented.