Optimal H _i / H _∞ fault‐detection filter design for uncertain linear time‐invariant systems: an iterative linear matrix inequality approach

Abstract

An iterative linear matrix inequality (LMI) approach is proposed to design fault-detection filters (FDFs) of uncertain linear time-invariant (LTI) systems. The obtained FDF is the optimal solution for the H i /H ∞ (with H ∞ /H ∞ and H − /H ∞ being two extreme cases) optimisation problem of FDF design and can achieve the best trade-off between robustness against unknown disturbances and sensitivity to system faults. The authors first derive the theoretical optimal H i /H ∞ FDFs for uncertain LTI systems based on the co-inner-outer factorisation technique. Then a new optimisation problem is formulated to obtain the optimal FDFs that can approach the theoretical optimal ones as much as possible. An iterative LMI approach is presented to find the solution in the state-space form. The effectiveness of the proposed approach is illustrated by a numerical example.

New results on robust stability analysis and synthesis for MIMO uncertain systems

“…In the literature, there exist many papers concerning the analysis and synthesis for continuous and discrete‐time systems, which propose several specific methodologies (see, e.g. [7–10, 19, 26–30, 33–40]).…”

A Survey on Model-Based Fault Detection Techniques for Linear Time-Invariant Systems with Numerical Analysis

“…Robust FD problem is formulated as model matching problem, and solution of the optimization problem is presented in linear matrix inequality (LMI) form in the said paper. Li et al (2013) extended the same work discussed in Ding et al (2000) for continuous-time linear uncertain systems subjected to polytopic uncertainty utilizing the iterative LMI approach. Farhat and Koenig (2015) formulated the proportional integral observer (PIO) design problem as a multi-objective optimization problem for the continuous-time linear uncertain system.…”

Multiple adaptive factors based interacting multiple model estimator

“…The concept of robust state estimation has been around for a long time, but its theory was formally introduced in the 1960s to address the instability issues in traditional optimization processes [7]. In the 1980s, Zames introduced the concept of $${H_\infty }$$ in control systems to reduce sensitivity to model uncertainties [8], which further led to the famous $${H_\infty }$$ estimation method and more related research [9–11]. Another important approach in robust state estimation is based on various improvements to the Kalman filter.…”