introduction to nonlinear system theory, examples of nonlinear systems (mechanical, electrical, hydraulic), stick-slip effect, basics of dynamical systems, existence and uniqueness of solutions, sensitivity equations, Lyapunov stability, invariance principle of Krasowskii-LaSalle, direct and indirect method of Lyapunov, Lyapunov equation, stability of non-autonomous systems, Lemma of Barbalat, singular perturbation theory, fast and slow manifold, boundary layer model, Theorem of Tikhonov, Lyapunov-based controller design (simple PD-law, computed torque, integrator backstepping, generalized backstepping, recursive backstepping), affine-input systems, exact input-output and input-state linearization of SISO- and MIMO-systems, relative degree, zero dynamics, trajectory tracking, flatness, basics of differential geometry (manifold, tangent and cotangent space, Lie derivatives, Theorem of Frobenius), observer design for linear time-variant systems
