Work

Feedback Stability Analysis via Frequency Dependent Constraints

Year: 2024

Type: article

Abstract: We establish robust stability of feedback interconnections of linear time-invariant systems with potentially marginally stable open-loop poles via frequency-varying quadratic constraints. These constraints may be used to characterise numerous system properties, such as small-gain, passivity, negative imaginariness, and their weighted variants, that are manifested on different band-limited frequencies. Such systems arise in practical mechanical settings where force actuators and displacement/velocity sensors are not colocated. We demonstrate that frequency-limited system properties may be characterised using the powerful Iwasaki–Hara lemma in terms of convex feasibility problems involving linear matrix inequalities, thereby complementing the utility of the Iwasaki–Hara lemma for robust feedback stability analysis involving mixed system properties on the frequency axis.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2024.3457432

Authors: Sei Zhen Khong, Alexander Lanzon

Institutions: National Sun Yat-sen University, University of Manchester

Language: English

Topic: Stability and Control of Uncertain Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science and Technology Council, National Science and Technology Council, Engineering and Physical Sciences Research Council

Awards: G2691329168, Robust feedback control of negative imaginary systems: From foundations to benchmark applications, Negative Imaginary Systems Control Theory and Its Applications in Complex Flexible Structures