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.

在本文中，提出了一种新颖的控制设计方法，该方法可确保多输入多输出离散时间线性多面体差异包含的瞬态性能。我们建立了一个定理，该定理为状态从状态空间的一个多面体子集演变为另一个提供了必要和充分的条件。然后，我们提出一种算法，该算法构造时变输出反馈定律，该定律可确保状态在时变多面体目标管内演化指定系统所需的瞬态性能。我们提出了涉及控制约束和有界加性扰动项的概括。我们的公式非常笼统，包括参考跟踪以及面对扰动时的任何所需瞬态行为，例如由最流行的阶跃响应规范所指定的。该方法通过一个涉及两个耦合罐中水位控制的示例进行了演示。