  In this paper a novel approach is presented for control design with
guaranteed transient performance for multiple-input multiple-output
discrete-time linear polytopic difference inclusions. 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. Then we present an algorithm
which constructs a time-varying output feedback law which guarantees that the
state evolves within a time-varying polyhedral target-tube specifying the
system's desired transient performance. We present generalisations involving
constraints on the control, and a bounded additive disturbance term. Our
formulation is very general and includes reference tracking with any desired
transient behaviour in the face of disturbances, as specified, for example, by
the most popular step response specifications. The approach is demonstrated by
an example involving the control of water levels in two coupled tanks.
