English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a dual form of Lyapunov-Krasovskii functional which allows theproblem of controller synthesis of multi-delay systems to be formulated andsolved in a convex manner. First, we give a general form of dual stabilitycondition formulated in terms of Lyapunov operators which are positive,self-adjoint and preserve the structure of the state-space. Second, we providea class of such operators and express the stability conditions as positivityand negativity of quadratic Lyapunov-Krasovskii functional forms. Next, weadapt the SOS methodology to express positivity and negativity of these formsas LMIs, describing a new set of polynomial manipulation tools designed forthis purpose. Finally, we apply the resulting LMIs to a battery of numericalexamples and demonstrate that the stability conditions are not conservative.The results of this paper are significant in that they open the way for dynamicoutput H-infinity optimal control of systems with multiple time-delays.

SOS Methods for Multi-Delay Systems: A Dual Form of Lyapanov-Krasovskii Functional