Calculation of the maximum absolute values of dynamical variables in linear control systems

In the analysis and design of linear control systems, we are often interested in the maximum absolute values of certain variables such as control inputs, state variables, or output variables. In other cases, we at least want to know whether the controller is admissible in the sense that inequality constraints given for these variables are always met. In this paper a computer oriented method is proposed, which makes it possible to calculate these maximum absolute values-or to establish admissibility-referring to all system trajectories starting in a certain region of the state space. This method can be applied to any finite dimensional continuous or discrete time linear control system and is proposed as a new tool for analysis and design.