Multi-Time-Scale Structure Assignment in Linear and Nonlinear Systems by High-Gain Feedback -- Singular Perturbation Approach

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This research will examine the role of time-scale structure in high-gain feedback systems and its relation to robustness of a design with respect to uncertainties and disturbances. Based on this, a novel concept of time-scale structure assignment for general dynamic systems is to be explored. Furthermore, unification and consequent generalization of various exisiting analysis and design of high-gain feedback methods is sought by casting them into the framework of singularly perturbed systems. Partitioning of a given design into subparts is facilitated through consistent exploitation of time-scale separation concepts embodied in singular perturbation theory. The specific problems which are to be examined are: (1) Eigenstructure assignment via quadratic regulator theory , (2) Direct methods of eigenstructure and multiple time-scale assignment in linear systems, (3) Almost disturbance decoupling with internal stability, (4) Guaranteed stability of uncertain systems, (5) Kalman filter with weak measurement noise, (6) Multiple time-scale assignment and shaping of slow and fast dynamics in nonlinear systems and (7) Nonlinear "cheap" control problems.