In control theory, my research is analysis and synthesis of control systems that give optimal performance given an approximate model of the physical system to be controlled. This is called ``Robust Control'' and it is an extremely important problem in practice since one rarely has an exact model for the physical system. My results have yielded conditions for the solvability of robust stabilization and disturbance rejection problems and constructive algorithms for solving these problems for various kinds of linear/nonlinear systems. My research is closely connected to H-infinity control, Linear Matrix Inequality approach for linear, nonlinear and multirate sampled-data systems. For nonlinear systems, Lyapunov's approach, backstepping, forwarding and other types of geometric approaches are also major theoretical tools.
One of my recent theoretical developments is the state-dependent scaling design for robust nonlinear systems control. The design framework encompasses a wide area of robust stabilization, tracking and disturbance attenuation of nonlinear systems subject to both static/parameter and dynamic uncertainties including unmodeled dynamics. The state-dependent scaling design can be considered as an extension of popular scaling techniques for linear systems to nonlinear systems. It also unifies various types and modifications of robust backstepping which was one of promising approaches for diverse nonlinear control problems. Another feature the state-dependent scaling design has on the other side is that it is amenable to numerical computation and optimization. It also guarantees the existence of analytical solutions for a class of nonlinear systems in a standard geometric structure.
For more details, you are invited to read my publications on these topics.