H. Freeman’s Discrete Time Systems – an introduction to the theory

Herbert Freeman’s book covers various topics including discrete time analysis, transformation calculus, sampling  continuous time functions, sampled data control systems, etc. Three treatments stand out: nonstationary linear discrete-time system solution, Laplace transform methods and a constructive method for Liapunov functions that are used to prove system stability.

The nonstationary discrete-time system equations (1-31) and (1-32) are:

The solution set (2-35), (2-36) and (2-37) is:

What is interesting about these equations is their wide applicability: from vehicle control to time-reversal mirror (TRM) performance. In the context of TRM, the solution enables modeling of cycle by cycle coherence formation. The Liapunov method can be applied to prove stability. Vehicle control stability is extensively studied and modeled. However, Freeman gives a good introduction for the uninitiated.