Robust Control Theory

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This project describes a basic research program focused on the design and analysis of robust and H- infinity optimal feedback systems. This research program has four major components: multivariable robust stability and stabilization problems, H-infinity optimal control of finite and infinite-dimensional systems, analysis and design of nonlinear time- varying controllers for robust control of linear time- invariant systems, controller design for multiple performance functionals. To account for possible uncertainties in system models, both parametric and unstructured uncertainty in plant models will be considered. Optimal design in the H-infinity norm is considered to provide robustness against uncertainty in the spectra of the exogenous signals or unstructured dynamic modeling uncertainty. It is also a key step in design for robust performance in the presence of unstructured uncertainty. The emphasis is on the development of computationally efficient algorithms for controller design. For this purpose, all high-level algorithms will be developed in terms state-space realizations, real or complex matrix algebraic equations, etc. It is expected that most of the algorithms will be implementable on a variety of computers ranging from engineering workstations to mainframe computers.