Control Design with Guaranteed Transient Performance via Reachable Set Estimates

We present a novel way of addressing the problem of control design with guaranteed transient performance for discrete-time linear systems. We establish a theorem that gives necessary and sufficient conditions for the state to evolve from one polyhedral subset of the state-space to another. An algorithm is then presented that, if executed successfully, produces a time-varying state-feedback control law along with a sequence of polyhedral sets within which the control law guarantees the state to evolve. The approach is demonstrated by an example involving the position control of a mass-spring-damper. We then point out various issues that may form the basis of future research.