A unified framework for control system synthesis
File(s)
Author(s)
Huang, Guilin
Type
Thesis
Abstract
Model-based control design in high-performance engineering is challenged by large state-space models, structured uncertainty, and the need to satisfy finite-frequency specifications that reflect actuator limits, perceptual thresholds, or regulatory windows. Requirements are often multi-objective and, in practice, solved with feasible but suboptimal designs, while theory prioritises new bounds and theorems. This thesis develops a unified, LMI-based framework that bridges this gap by treating multiple design problems—controller synthesis, model order reduction, and observer-based fault detection/reconstruction, under exact frequency-interval specifications without weighting filters.
The framework uses the generalised KYP lemma and a separation technique with the projection lemma to linearise nonlinear matrix inequalities into tractable LMIs without imposing a common Lyapunov variable or fixing controller order. Monotone algorithms are provided to guarantee non-increasing performance indices and provide numerically efficient procedures for state-feedback, static output-feedback, and dynamic output-feedback.
For model order reduction, the method delivers frequency-interval \(H_\infty\) error guarantees and extends it to systems with norm-bounded uncertainty, yielding a single reduced-order model valid across admissible uncertainties, with optional stability enforcement.
For fault detection and reconstruction, the framework poses mixed \(H^{-}\)/\(H_\infty\) objectives on different channels over designer-chosen frequency intervals, enabling disturbance attenuation and fault sensitivity, and supports reconstruction of steady-state fault signals using a Fourier-based residual method.
Finally, the framework is extended to Lur’e-type nonlinear systems, where finite-frequency design improves closed-loop performance analogously to the LTI case. Numerical studies demonstrate predictable performance improvements, robustness across low-, mid- and high-frequency intervals, and practical tractability for high-order plants.
The framework uses the generalised KYP lemma and a separation technique with the projection lemma to linearise nonlinear matrix inequalities into tractable LMIs without imposing a common Lyapunov variable or fixing controller order. Monotone algorithms are provided to guarantee non-increasing performance indices and provide numerically efficient procedures for state-feedback, static output-feedback, and dynamic output-feedback.
For model order reduction, the method delivers frequency-interval \(H_\infty\) error guarantees and extends it to systems with norm-bounded uncertainty, yielding a single reduced-order model valid across admissible uncertainties, with optional stability enforcement.
For fault detection and reconstruction, the framework poses mixed \(H^{-}\)/\(H_\infty\) objectives on different channels over designer-chosen frequency intervals, enabling disturbance attenuation and fault sensitivity, and supports reconstruction of steady-state fault signals using a Fourier-based residual method.
Finally, the framework is extended to Lur’e-type nonlinear systems, where finite-frequency design improves closed-loop performance analogously to the LTI case. Numerical studies demonstrate predictable performance improvements, robustness across low-, mid- and high-frequency intervals, and practical tractability for high-order plants.
Version
Open Access
Date Issued
2025-08-16
Date Awarded
2026-05-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Jaimoukha, Imad
Publisher Department
Department of Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)