My research is generally concerned with analysis and synthesis of control systems that give optimal or resilient performance to physical system. There, robustness is an extremely important problem in practice since one rarely has an exact mathematical model for the physical system. My research results have yielded conditions for the solvability of robust stabilization and disturbance rejection problems and constructive algorithms for solving those problems for various kinds of linear and nonlinear systems. My research is closely connected to H-infinity control, Linear Matrix Inequality approach for linear, nonlinear and multirate sampled-data systems. My current field of leading research topics are in nonlinear systems control. Lyapunov's approach, dissipation analysis, input-to-state stability, backstepping, forwarding and other types of geometric approaches are also major theoretical tools.
One of my major theoretical developments is the state-dependent scaling framework for module-based design and analysis of dynamical systems and networks. The framework helps to solve many problems in 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 can be regarded as a ``global'' extension of popular scaling techniques for linear systems to nonlinear systems to truly go beyond Jacobian analysis. 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 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 lot of classes of nonlinear systems including time-delay systems, distributed parameter systems, and stochastic dynamical systems.
For more details, you are invited to read my publications on these topics.
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