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Discrete-time Systems and Lyapunov Theory
This lecture covers the review of linear discrete-time systems and Lyapunov theory. It starts by introducing the concept of equilibria and stability in linear time-invariant (LTI) systems in discrete time. The stability test through Lyapunov functions is explained, along with the definitions of stability in linear time-varying (LTV) systems. The lecture also delves into the stability of equilibria of LTI systems and the relevant properties. Lyapunov stability theory is discussed, focusing on the stability of the origin for LTI systems. The lecture concludes with a review of positive-definite matrices, quadratic functions, and Lyapunov theorems.