Syllabus

Signals and systems, Vector space, Norms, Matrix theory: Inversion formula, Schur’s complement, Singular Value Decomposition, Positive definiteness; Linear Matrix Inequality: Affine function, Convexity, Elimination lemma, S‐procedure; Calculus of variation, Euler’s Theorem, Lagrange multiplier. Linear fractional transformation (LFT), Different uncertainty structures: Additive, Multiplicative, Uncertainty in Coprime factors; Concept of loop shaping, Bode’s Gain and phase relationship, Small Gain theorem. LQR, LQG, Hamiltonian matrix, Riccati equation, H‐infinity control, H‐infinity Controller design via DGKF and LMI techniques, H‐infinity loop shaping technique, Structured singular value (mu) synthesis, Design examples.