A Convex Reformulation of the Controller Synthesis Problem for Infinite-Dimensional Systems using Linear Operator Inequalities (LOIs) with Application to MIMO Multi-Delay Systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

In this paper, we propose a formal duality and operator-based framework for controller synthesis of infinite-dimensional systems using convex optimization. Specifically, we propose a class of what we call Linear Operator Inequalities (LOIs) and give conditions under which LOIs are solvable and under which they can be used for controller synthesis. Within this LOI framework, the first technical contribution of the paper is a new dual stability condition under which we can reformulate the controller synthesis problem as an LOI. The second technical contribution is LOIs for both primal and dual stability of systems with multiple delays. The third technical contribution is to show that both these LOIs are solvable. Finally, we use an LMI-based framework to solve these LOIs and demonstrate numerically that the primal and dual stability conditions are functionally equivalent for MIMO systems with multiple delays.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3322-3329
Number of pages8
Volume2018-June
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

Fingerprint

MIMO systems
Controllers
Convex optimization

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Peet, M. (2018). A Convex Reformulation of the Controller Synthesis Problem for Infinite-Dimensional Systems using Linear Operator Inequalities (LOIs) with Application to MIMO Multi-Delay Systems. In 2018 Annual American Control Conference, ACC 2018 (Vol. 2018-June, pp. 3322-3329). [8430836] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8430836

A Convex Reformulation of the Controller Synthesis Problem for Infinite-Dimensional Systems using Linear Operator Inequalities (LOIs) with Application to MIMO Multi-Delay Systems. / Peet, Matthew.

2018 Annual American Control Conference, ACC 2018. Vol. 2018-June Institute of Electrical and Electronics Engineers Inc., 2018. p. 3322-3329 8430836.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Peet, M 2018, A Convex Reformulation of the Controller Synthesis Problem for Infinite-Dimensional Systems using Linear Operator Inequalities (LOIs) with Application to MIMO Multi-Delay Systems. in 2018 Annual American Control Conference, ACC 2018. vol. 2018-June, 8430836, Institute of Electrical and Electronics Engineers Inc., pp. 3322-3329, 2018 Annual American Control Conference, ACC 2018, Milwauke, United States, 6/27/18. https://doi.org/10.23919/ACC.2018.8430836
Peet M. A Convex Reformulation of the Controller Synthesis Problem for Infinite-Dimensional Systems using Linear Operator Inequalities (LOIs) with Application to MIMO Multi-Delay Systems. In 2018 Annual American Control Conference, ACC 2018. Vol. 2018-June. Institute of Electrical and Electronics Engineers Inc. 2018. p. 3322-3329. 8430836 https://doi.org/10.23919/ACC.2018.8430836
Peet, Matthew. / A Convex Reformulation of the Controller Synthesis Problem for Infinite-Dimensional Systems using Linear Operator Inequalities (LOIs) with Application to MIMO Multi-Delay Systems. 2018 Annual American Control Conference, ACC 2018. Vol. 2018-June Institute of Electrical and Electronics Engineers Inc., 2018. pp. 3322-3329
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