Discrete-time Systems: Z-transform and Stability

This lecture covers the Z-transform of signals, poles and zeros of rational functions, stability analysis based on pole locations, and the impact of poles on system response. The instructor explains the process of finding transfer functions, implementing controllers in discrete-time systems, and the importance of choosing the right sampling period. Various methods for discretizing continuous systems are discussed, including impulse and step responses, and the implications of different approximation techniques for derivatives. The lecture also delves into the Nyquist theorem, loop shaping, and the design of digital controllers. Practical considerations for implementing controllers, such as the choice between zero-order hold and first-order hold, are explored.