Low-order stabilizers for linear systems

Abstract

The existence and construction of low-order stabilizers for linear systems are considered. Firstly, it is shown that for an all-pole plant the stability of the high-degree part of the plant transfer function's denominator guarantees the existence of a low-order stabilizer. Secondly, if this high-degree part is unstable, a method is presented to modify it such that the above result is applicable. Thirdly, an algorithm for constructing a low-order stabilizer for a general plant is developed where only a few linear algebraic equations need be solved. Several examples are included for illustration of the results.