Homogeneity-Based Design of High-Order Sliding Mode Observers for MEMS Resonators
Prof. Alexander Triana, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia

Abstract: This talk presents a robust observer-design framework for MEMS resonators based on high-order sliding modes (HOSM), emphasizing homogeneity as the central tool for both analysis and synthesis. The motivation arises from the well-known limitations of classical first-order sliding mode methods, which, despite their robustness, suffer from chattering, sensitivity to measurement noise, and relative-degree restrictions. The main contribution of the talk is to show how homogeneity provides a unifying framework for HOSM observer design by linking classical, weighted, and geometric homogeneity with finite-time stability analysis of discontinuous systems through homogeneous vector fields and their Filippov regularizations. This perspective is further connected to finite-time and fixed-time stability, as well as robustness properties of ISS/iISS type, highlighting why homogeneity is especially effective for observer synthesis in nonlinear uncertain systems. Overall, the talk argues that homogeneity is not only a theoretical concept, but a practical design principle for constructing finite-time, robust, and implementable observers for MEMS resonator applications.

Speaker's Bio: Alexander Jiménez Triana is a Professor and Researcher with more than twenty years of academic and scientific experience in nonlinear systems and robust control, with a strong emphasis on sliding mode control and active disturbance rejection control. He holds Ph.D. degrees in Electrical Engineering from École Polytechnique de Montréal (Canada) and Universidad de los Andes (Colombia), and he is currently a full-time professor at Universidad Distrital Francisco José de Caldas. He has also held international positions, including a Research Fellow appointment at City University of Hong Kong and an invited professorship at École Polytechnique de Montréal. His work includes peer-reviewed publications, international conference participation, and leadership of research projects in robust control and related engineering applications.