Backward Linear Control Systems on Time Scales

TL;DR

This paper develops a linear control systems theory on arbitrary time scales using backward nabla derivatives and Caputo's duality, establishing controllability, observability, and realizability criteria.

Contribution

It introduces a novel approach to control systems on time scales via backward nabla derivatives and duality, extending classical control theory results.

Findings

Kalman controllability and observability criteria are established.

Realizability conditions for backward control systems are proved.

A unified framework for control systems on arbitrary time scales is provided.

Abstract

We show how a linear control systems theory for the backward nabla differential operator on an arbitrary time scale can be obtained via Caputo's duality. More precisely, we consider linear control systems with outputs defined with respect to the backward jump operator. Kalman criteria of controllability and observability, as well as realizability conditions, are proved.