Reduced-order output feedback controllers for discrete-time systems

This article considers the stabilization by output feedback controllers for discrete-time systems. The controller can place all of the closed-loop poles within a specified disk D(-α, 1/β), centred at (-α,0) with radius 1/β, where | - α|  + 1/β < 1. The design method involves the decomposition of the system into two portions. The first portion comprises of all of the poles that are lying outside of the specified disk. A reduced-order model is constructed for this portion. The second portion comprises of all of the remaining poles of the system and is characterized by an H_∞-norm bound. The controller design is then accomplished by using H_∞-control theory. It is shown that, subject to the solvability of an algebraic Riccati equation, output feedback controllers can be systematically derived. The order of the controller is low, and can be as low as the number of the open-loop poles that are lying outside of the specified disk. A step-by-step design algorithm is provided. Numerical examples are given to illustrate the attractiveness of the design method.