Research Interests in Brief

My research interests lie at the intersection of nonlinear dynamical systems, control theory, contraction analysis, multistability, chaos theory, and optimization. I am particularly interested in developing rigorous analytical tools based on contraction theory, 2-contraction, additive compound matrices, Lyapunov methods, and basin-of-attraction analysis to study the qualitative behavior of nonlinear systems with multiple equilibria, periodic forcing, and complex transient dynamics. I also have expertise in chaos control and chaos synchronization, with special emphasis on reduced-order synchronization, projection-based synchronization strategies, and control mechanisms for complex chaotic systems. My work focuses on applying these ideas to problems in epidemic modeling, synchronization of multistable networks, power electronic converters, nonconvex optimization, and control-theoretic analysis of learning algorithms. A central goal of my research is to design mathematically certified methods that can guarantee stability, exclude chaotic or oscillatory behavior, characterize convergence regions, and improve the reliability of nonlinear systems arising in engineering and applied sciences.