Robust Control
- Overview of robust control
- Introduction on linear algebra & linear dynamical systems
- Linear spaces, Inner-product spaces, Hilbert spaces, Banach spaces, H_2 and H_infinity spaces, norms of signals and systems, Relation between signals and systems norm, Computing H_2 and H_infinity norms, Frequency-domain interpretation of H_infinity norm, Time-domain interpretation of H_infinity norm
- Internal stability, Well-posedness, Coprime Factorization, Plant factorization, Coprime Factorization of a stabilizing controller
- Performance Specifications, Feedback properties, performance tradeoffs & design limitations, sensitivity transfer matrices, Weighted H_2 & H_? problems, H_2& H_? mixed-sensitivity, analyticity or interpolation conditions, waterbed effect.
- Modeling uncertainty and robustness, representation of uncertainties, structured and unstructured uncertainties, parameterized, additive and multiplicative uncertainties, Robust Stability, Robust Performance, Small-gain Theorem , Robustness for Unstructured Uncertainties
- Linear Fractional Transformation (LFT), Formulation of control problems in LFT framework, parameterization of all stabilizing controller,
- mu synthesis, structured singular value, structured robust stability, robust performance
- Algebraic Riccati Equations (AREs), stabilizing solutions for ARE, Bounded Real Lemma (BRL)
- H_infinity control problem
- Introduction to convex optimization, introduction to Linear Matrix Inequalities (LMIs), application of LMIs in H_2 & H_infinity optimal control problems