Robust observer design for a class of nonlinear systems: LMI approach

Sammanfattning: Observer design for nonlinear systems is a well-known problem in control theory that has been studied from different perspectives. Because the system state variables are generally not always available, state estimation is an essential task in many control applications, which is why this problem has attracted considerable attention from researchers and is the main focus of this thesis.Knowing that no mathematical system can exactly model a physical system, as a control engineer we must be aware of how modeling errors might adversely affect the performance of a control system. From the observer perspective, time-delays, uncertainties and unknown inputs are familiar factors that deteriorate the observer performance on the way of design, analysis and synthesis of any type of observer. Every general observer design should be able to treat all (or at least some) of these issues explicitly and provide quantitative and qualitative results about their impact on the observer performance: consequently, the concepts of robustness, robust performance and robust design have recently become common phrases in the literature and constitute an integral part of research on observer design.Compared to the typical linear systems, observer design for nonlinear systems subject to all the aformentioned deteriorative properties presents a greater challenge for control engineers and researchers. In this thesis, the problem of observer design for a class of nonlinear systems, both discrete and continuous-time, subject to time delay, structured uncertainty and unknown inputs, is investigated. The study shows that by using the upper and lower bounds of the time delay, this parameter can be excluded in the observer structure under some constraints. Moreover, a novel method for designing an Unknown Input Observer (UIO) for a class of nonlinear systems is proposed, which makes the observer capable to satisfy desired performance even inthe presence of unknown inputs. Based on the UIO structure, one step further is taken, and a multiobjective optimization approach for state estimation and unknown input reconstruction is proposed that makes the designed observer not only robust against unknown inputs but also able to reconstruct them under some provided linear matrix inequality (LMI) conditions. In light of linear algebra, note that LMI serves as an important tool in this thesis, significantly facilitating the proposed observer designs.