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Related papers: Converse negative imaginary theorems

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Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…

Optimization and Control · Mathematics 2022-11-15 Saman Cyrus , Laurent Lessard

A robust output feedback consensus problem for networked identical nonlinear negative-imaginary (NI) systems is investigated in this paper. Output consensus is achieved by applying identical linear output strictly negative-imaginary (OSNI)…

Systems and Control · Electrical Eng. & Systems 2021-04-09 Kanghong Shi , Igor G. Vladimirov , Ian R. Petersen

Passivity is an imperative concept and a widely utilized tool in the analysis and control of interconnected systems. It naturally arises in the modelling of physical systems involving passive elements and dynamics. While many theorems on…

Optimization and Control · Mathematics 2017-01-03 Sei Zhen Khong , Arjan van der Schaft

This paper presents some physical interpretations of recent stability results on the feedback interconnection of negative imaginary systems. These interpretations involve spring mass damper systems coupled together by springs or RLC…

Systems and Control · Computer Science 2015-03-05 Ian R. Petersen

Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…

Optimization and Control · Mathematics 2019-09-18 Saman Cyrus , Laurent Lessard

The negative imaginary (NI) systems theory has attracted interests due to the robustness properties of feedback interconnected NI systems. However, a full output optimal controller-synthesis methodology, for such class of systems, is yet to…

Optimization and Control · Mathematics 2022-04-05 Mohamed Mabrok

The recent rapid proliferation of renewable energy is fundamentally changing the dynamic operations of power systems, necessitating new approaches to assess stability for these highly nonlinear systems. In this paper, we prove that…

Systems and Control · Electrical Eng. & Systems 2026-05-07 Maryam Khodabakhshloo , Elizabeth L. Ratnam , Ian R. Petersen

Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…

Optimization and Control · Mathematics 2022-08-15 Rania Tafat , Thomas Göhrt , Stefan Streif

This paper presents a method for the synthesis of negative imaginary closed-loop systems with a prescribed degree of stability under the assumption of full state feedback. The approach extends existing work by using a perturbation method to…

Optimization and Control · Mathematics 2018-07-20 James Dannatt , Ian Petersen

The robust stability problem involves designing a controlled system which remains stable in the presence of modeling uncertainty. In this context, results known as small gain theorems are used to quantify the maximum amount of uncertainty…

Optimization and Control · Mathematics 2026-04-01 Gavin Glenn , Emma J. Reid

We prove the following converse of the passivity theorem. Consider a causal system given by a sum of a linear time-invariant and a passive linear time-varying input-output map. Then, in order to guarantee stability (in the sense of finite…

Optimization and Control · Mathematics 2018-09-05 Sei Zhen Khong , Arjan van der Schaft

In this paper, we show that a hybrid integrator-gain system (HIGS) is a nonlinear negative imaginary (NNI) system. We prove that the positive feedback interconnection of a linear negative imaginary (NI) system and a HIGS is asymptotically…

Systems and Control · Electrical Eng. & Systems 2023-03-24 Kanghong Shi , Nastaran Nikooienejad , Ian R. Petersen , S. O. Reza Moheimani

Incremental stability properties are considered for certain systems of forced, nonlinear differential equations with a particular positivity structure. An incremental stability estimate is derived for pairs of input/state/output…

Systems and Control · Electrical Eng. & Systems 2024-02-07 Violaine Piengeon , Chris Guiver

This paper provides a protocol to address the robust output feedback consensus problem for networked heterogeneous nonlinear negative-imaginary (NI) systems with free body dynamics. We extend the definition of nonlinear NI systems to allow…

Systems and Control · Electrical Eng. & Systems 2021-07-02 Kanghong Shi , Ian R. Petersen , Igor G. Vladimirov

This paper provides a control protocol for the robust output feedback consensus of networked heterogeneous nonlinear negative-imaginary (NI) systems. Heterogeneous nonlinear output strictly negative-imaginary (OSNI) controllers are applied…

Systems and Control · Electrical Eng. & Systems 2021-04-07 Kanghong Shi , Igor G. Vladimirov , Ian R. Petersen

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…

Optimization and Control · Mathematics 2024-12-03 Thomas Chaffey , Andrey Kharitenko , Fulvio Forni , Rodolphe Sepulchre

State convergence is essential in several scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, monotone game theory, multi-agent learning over time-varying networks. This paper is the first on state…

Optimization and Control · Mathematics 2019-10-02 Filippo Fabiani , Giuseppe Belgioioso , Franco Blanchini , Patrizio Colaneri , Sergio Grammatico

In the context of linear control systems, a commonly-held intuition is that negative and positive feedback cannot both be stability enhancing. The canonical linear prototype is the scalar system $\dot x=u$ which, under negative linear…

Optimization and Control · Mathematics 2026-02-23 Thomas Berger , Achim Ilchmann , Eugene P. Ryan

For a non-linear MIMO feedback system, the robustness against uncertain time-variations in the feedback loop is investigated in an input-output framework. A general sufficient condition in terms of a bound on average rates of time-variation…

Systems and Control · Electrical Eng. & Systems 2020-03-03 Yu-chen Sung , Sagar V. Patil , Michael G. Safonov

This paper addresses the problem of stabilization for infinite-dimensional systems. In particular, we design nonlinear stabilizers for both linear and nonlinear abstract systems. We focus on two classes of systems: the first class comprises…

Systems and Control · Electrical Eng. & Systems 2025-09-19 Kamal Fenza , Moussa Labbadi , Mohamed Ouzahra