Basics: Control system representations, System stabilities, Coprime factorization and stabilizing controllers, Signals and system norms Modelling of uncertain systems: Unstructured Uncertainties, Parametric uncertainty, Linear fractional transformation, Structured uncertainties.

Robust design specifications: Small gain theorem and robust stabilization, Performance considerations, Structured singular values.

Design:Mixed sensitivity optimization, 2-Degree of freedom design, Sub-optimal solutions, Formulae for discrete time cases.

Loop-shaping design procedures:Robust stabilization against Normalized coprime factor perturbation, Loop shaping design procedures, Formulae for discrete time cases. m-Analysis and Synthesis: Consideration of robust performance, m-synthesis: D-K iteration method, m-synthesis: m -K iteration method.

Lower-order controllers:Absolute error approximation methods like Balanced truncation, Singular perturbation approximation and Hankel-norm approximation, Reduction via fractional factors, Relative error approximation and frequency weighted approximation methods.

Design case studies:Robust Control of a mass damper spring system, A triple inverted pendulum control system, Robust control of a hard disk drive.

Linear Matrix Inequalities:Some standard LMI problems –eigen-value problems,generalisedeigen-value problems; Algorithms to solve LMI problems –Ellipsoid algorithm, interior point methods

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2.Alok Sinha, Linear Systems-Optimal and Robust Controls, CRC Press, 2007.

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