Course Details

Course details of EE5413
Course NoEE5413
Course TitleLinear Dynamical Systems
Course Content1. Models of physical and biological systems-- simple pendulum, segway scooter, consensu protocols for sensor networks, gene regulatory networks2. Equilibrium/operating points, Jacobian linearization3. Relative degree, diffeomorphism, input/output linearization of nonlinear systems4. Minimal realization, Smith-McMillan form5. Continuous-time linear time-varying/time-invariant (LTV/LTI) state-space models, Peono-Baker series, matrix exponentials, similarity transformations, Jordan normal form, algebriac and geometric multiplicity, minimal polynomial6. Reachable and controllable subspaces, Controllability and observability Gramians, Kalman and Popov-Belevitch-Hautus (PBH) test for controllability and observability, Controllable and observable canonical forms7. Stabilizability and detectability, Kalman canonical decomposition, Review of matrix theory--matrix norms, positive/negative definiteness8. Lyapunov stability, Lyapunov equation, Eigenvalue conditions for Lyapunov stability, Separation principle, pole-placement and observer design9. Linear optimal control techniques, Linear quadratic regulator (LQR), the algebraic Riccati equation.
Course Offered this semesterNo
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