Robust and Reduced Order H-Infinity Filtering via LMI Approach and Its Application to Fault Detection

Abstract

The objective of this dissertation is to develop a practical methodology for designing full and reduced order H filter for plants with polytopic model uncertainty. Because the polytopic ∞ model description is convex, it is amenable to a Linear Matrix Inequality (LMI) formulation. Reduced order filters are desirable in applications where fast data processing is necessary. To improve robustness to model uncertainties, this dissertation reformulates an filter design 2 H technique as a reduced order H filter design methodology. Lyapunov functions are replaced ∞ with parameter-dependent Lyapunov functions to provide less conservative results. As the problem is formulated as an LMI, an admissible filter with suitable dynamic behavior can be obtained from the solution of a convex optimization problem. The advantages of this approach over earlier approaches are highlighted in a simple computational example. This filtering technique is used to design a fault detection filter. Robust fault detection filter (RFDF) design is formulated as a multi-objective H∞ optimization for a polytopic uncertain system. The order of the RFDF is reduced using LMI techniques and the detection performance is compared with the full order filter. An adaptive threshold is used to reduce the number of false alarms. Examples are presented to illustrate effectiveness of the order reduction.