On the active nodes of network systems
File(s)
Accepted version
Author(s)
Chen, Kaiwen
Astolfi, Alessandro
Type
Conference Paper
Abstract
This paper studies interconnected systems (nodes) and exploits dissipation inequalities and the structure of the interconnection (the network) to derive analysis and design tools for stabilization. First, systems with quadratic supply rates in the dissipation inequalities are investigated. A stability condition based on the dissipation inequality associated to each node is given. This condition allows checking the sign of the dissipation inequality for the overall network system. By considering the underlying directed graph, the feasibility of controller design is discussed. The design problem is re-formulated into the problem of finding a solution to a system of linear inequalities. This allows the efficient search and computation of the design parameters of what we call active nodes. Then, systems with non-quadratic supply rates are considered. A vector of positive definite functions that is used as a basis of the non-quadratic supply rates is constructed: this requires augmenting the underlying directed graph. Similarly to the quadratic supply rates case, a stability condition for analysis and a graph-based criterion for checking the feasibility of controller design are discussed. Finally a design example to demonstrate how to exploit the so-called active nodes to design a controller without numerical computation is presented. The proposed method does not presume any stability property of the nodes and therefore can be applied to various scenarios occurring in the study of stability properties for network systems.
Date Issued
2021-01-11
Date Acceptance
2020-12-01
Citation
2020 59th IEEE Conference on Decision and Control (CDC), 2021, pp.5561-5566
ISSN
0743-1546
Publisher
IEEE
Start Page
5561
End Page
5566
Journal / Book Title
2020 59th IEEE Conference on Decision and Control (CDC)
Volume
2020-December
Copyright Statement
Copyright © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Source
59th IEEE Conference on Decision and Control (CDC)
Subjects
Automation & Control Systems
CONSTRUCTION
Engineering
Engineering, Electrical & Electronic
IISS
LYAPUNOV FORMULATION
Science & Technology
SMALL-GAIN
STABILITY
Technology
Publication Status
Published
Start Date
2020-12-14
Finish Date
2020-12-18
Coverage Spatial
Jeju, Korea (South) (Virtual)