Background on Lyapunov Stability and Stochastic Optimal Control
This part of the chapter is from Sarangapani (2006). Many systems in nature, including neurobiological systems, are dynamical in nature, in the sense that they are acted upon by external inputs, have internal memory, and behave in certain ways that are captured by the notion of the development of activities through time. According to the notion of systems defined by Whitehead (1953), it is an entity distinct from its environment, whose interactions with the environment can be characterized through input and output signals. An intuitive feel for dynamic systems is provided by Luenberger (1979), which includes many examples.