Forward-complete systems

Abstract

As we have seen in Chapter 10, the predictor feedback has no chance of achieving global stability for systems that are prone to finite escape in an open loop, which is due to the absence of control during the actuator’s “dead time”. For this reason, in this chapter we focus on the class of forward-complete systems, which are guaranteed to have solutions that remain bounded (despite a possible exponential instability) for all finite time, as long as the input remains finite. This is not a small class of systems. It includes all linear systems–both stable and unstable. It also includes various nonlinear systems that have linearly bounded nonlinearities, such as systems in mechanics that contain trigonometric nonlinearities, as a result of rotational motions.