Analog algorithms with discontinuous states and non-unique evolution operators: Computability and stability

In this work computability and stability issues for analog algorithms with discontinuous states and non-unique evolution operators are studied. The notions of analog algorithm and dynamical system are postulated to be equivalent. The stability and stabilization concepts for analog algorithms are defined. The stability and stabilization presentation starts concentrating in continuous and discrete dynamical systems i.e., analog algorithms, defined by differential or difference equations, and continues considering Lyapunov energy functions for analog algorithms with continuous and discontinuous states. Dynamical systems with non-unique evolution operators are also studied.