Properties and stability analysis of discrete-time negative imaginary systems

DOI10.1016/J.AUTOMATICA.2017.05.006zbMath1373.93204OpenAlexW2622278073MaRDI QIDQ1679074

Mei Liu, Junlin Xiong

Publication date: 8 November 2017

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2017.05.006

zbMATH Keywords

discrete-time systemsinternal stabilitypositive feedbacknegative imaginary lemma

Mathematics Subject Classification ID

Discrete-time control/observation systems (93C55) Stability of control systems (93D99)

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Robust formation control for networked robotic systems using negative imaginary dynamics ⋮ Phases of discrete-time LTI multivariable systems ⋮ Static output feedback negative imaginary controller synthesis with an \(H_\infty\) norm bound ⋮ Static output feedback negative imaginary controller design with H ₂ performance ⋮ Finite, fixed and prescribed-time stability and stabilization of nonlinear negative imaginary systems ⋮ A negative imaginary lemma and state-feedback negative imaginary synthesis for commensurate fractional-order systems ⋮ Strictly negative imaginary state feedback control with a prescribed degree of stability ⋮ On positive realness, negative imaginariness, and \(H_\infty\) control of state-space symmetric systems ⋮ Negative imaginary synthesis via dynamic output feedback and static state feedback: a Riccati approach ⋮ Robustness analysis of the feedback interconnection of discrete-time negative imaginary systems via integral quadratic constraints ⋮ Applying negative imaginary systems theory to non-square systems with polytopic uncertainty ⋮ Necessary and sufficient conditions for lossless negative imaginary systems ⋮ Controller synthesis for negative imaginary systems using nonlinear optimisation and H₂ performance measure ⋮ On positive realness and negative imaginariness of uncertain discrete-time state-space symmetric systems ⋮ Interval frequency negative imaginary systems

Cites Work

• Preservations of positive realness under discretizations
• Generalizing Negative Imaginary Systems Theory to Include Free Body Dynamics: Control of Highly Resonant Structures With Free Body Motion
• Bilinear Transformation of Infinite-Dimensional State-Space Systems and Balanced Realizations of Nonrational Transfer Functions
• Stability Robustness of a Feedback Interconnection of Systems With Negative Imaginary Frequency Response
• Stability Analysis for a String of Coupled Stable Subsystems With Negative Imaginary Frequency Response
• A Negative Imaginary Lemma and the Stability of Interconnections of Linear Negative Imaginary Systems
• Stability Analysis of Interconnected Systems With “Mixed” Negative-Imaginary and Small-Gain Properties
• Dissipative systems analysis and control. Theory and applications
• On non-proper negative imaginary systems

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