A decision functional for multitime controllability

TL;DR

This paper explores the controllability of multitime linear PDE systems, introducing new theoretical tools such as the gamma-gramian matrix and controllability functional, supported by illustrative examples.

Contribution

It presents novel controllability criteria for multitime PDE systems using the gamma-gramian and introduces a new controllability functional.

Findings

Controllability characterized via gamma-gramian matrix

Introduction of a new controllability functional

Illustrative examples demonstrating theoretical results

Abstract

This paper investigates the multitime linear normal PDE systems. We study especially the controllability of such systems, obtaining complementary results to those in our recent papers. Here the multitime controllability original results are formulated using the $\gamma$ - gramian matrix, the Im - gramian space and a controllability functional. There are given also some original examples which illustrate and round the theoretical results.