Singular Value Assignment for Nonuniformly Sampled Systems: Stabilization and Control

TL;DR

This paper introduces a singular value assignment method for designing state feedback controllers that ensure stability of nonuniformly sampled systems, allowing for arbitrary sampling periods within an interval and potential performance improvements.

Contribution

It presents a novel controller design approach using singular value assignment to guarantee stability under nonuniform sampling and explores performance enhancement options.

Findings

Stability guaranteed for arbitrary sampling periods within an interval.

Existence of such an interval for stabilizable continuous systems.

Method can improve system performance by selecting specific singular values.

Abstract

A state feedback controller design is proposed to guarantee stability of a nonuniformly sampled system for arbitrary selections of sampling periods within an interval, assuming the controller can select the sampling period. It is also shown that such an interval always exists when the continuous time system - that is to be sampled nonuniformly - is stabilizable. The proposed method uses singular value assignment to guarantee the stability. Also, special selections for desired singular values are provided to demonstrate that this method can also be used to improve the performance at the expense of the maximum sampling period.