Additional stability results with bounded controls

This note is a simplified version of Teel (1994), it discusses, on a less technical level, only those problems that are closely related to the control of linear systems. Three results are presented. The first is that, for linear systems asymptotically null controllable with bounded controls, global asymptotic stability can be achieved which is robust to a class of stable nonlinear dynamic perturbations driven by the input. The second result is that the domain of attraction which can be achieved for an exponentially unstable system with a `nice´ bounded control is limited only by the domain of attraction which can be achieved with a `nice´ bounded control for the unstable subspace. As a simple example, the author discusses the linearized model of the inverted pendulum on a cart. The third result is that linear systems with simultaneous actuator rate and magnitude saturation and small time delays are no more difficult to globally asymptotically stabilize than linear systems with actuator magnitude saturation only