Continuous-Time Linear Dynamical Systems

Abstract

Here we consider observed and controlled linear dynamical systems in continuous-time. Real systems are rarely linear; they often involve nonlinear behaviors described by nonlinear terms in the dynamical equations of the model. However, the interest of linear dynamical systems is emphasized at the end of this chapter. Indeed, we show that the study of the tangent linear system generally makes it possible to locally stabilize an equilibrium of the nonlinear original system. In contrast to Chaps. 2 and 4, where only two types of variables were considered, namely the state vector and the external input variables, we are now going to take into account output or observed variables which constitute the components of the state directly measured through sensors.