I enjoy working in mathematical theory of systems and control. The research in this area addresses the mathematical foundations of nonlinear system analysis and feedback control. Nonlinear control theory is of central importance to application areas ranging from mechanical and aerospace engineering to chemical engineering, physics, and biology, and the study of the associated mathematical theory is of uttermost relevance.
There are in general two primary components in control system designs: the first one is to design for a given system a control law to guide the system to a desired performance; and the second one is to analyze the performance of the system under the control law. My work focuses in the second component. To be more specific, most of my work deals with stability analysis. This is an exciting area where engineering problems often lead to interesting mathematical problems. My recent work deals with stability analysis for systems that are affected by time delays and disturbances.