The Behavioural Approach to Systems and Control

The purpose of this paper is to provide an informal introduction to the behavioural approach to systems and control. We start with some historical observations. Then we turn to the modelling of dynamical systems and argue that interconnected systems lead to models involving both manifest and latent variables, but which are a far distance from an input/output or a state space description. Subsequently, control questions will be formulated in this setting. As a particular application, we discuss the eigenvalue assignment for linear time-invariant systems. The paper closes with an example of the stabilization of an inverted pendulum

Stability of Forced Higher-Order Continuous-Time Lur'e Systems: a Behavioural Input-Output Perspective

We consider a class of forced continuous-time Lur'e systems obtained by applying nonlinear feedback to a higher-order linear differential equation which defines an input-output system in the sense of behavioural systems theory. This linear system directly relates the input and output signals and does not involve any internal, latent or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability and strong integral input-to-output stability, concepts which are very much reminiscent of input-to-state stability and strong integral input-to-state stability, respectively. The methods used in the paper combine ideas from the behavioural approach to systems and control, absolute stability theory and input-to-state stability theory