Contents 1. Introduction
Because of their wide range of applicability, hybrid switching diffusion systems have drawn growing attention especially in the fields of control and optimization recently, Such systems are capable of describing complex systems and their inherent uncertainty and randomness in the environment; the formulation is versatile and provides more opportunity for realistic modeling, but adds substantial difficulties in the analysis. Much of the study comes from applications arising in control engineering, manufacturing systems, estimation, identification, and filtering, two-time-scale systems, and financial engineering; see for example, [11], [14], [20], [21], [22], [26], [28], [30], [37], among others. Random-switching processes are used to model demand rate or machine capacity in production planning, to describe the volatility changes over time to capture discrete shifts such as market trends and interest rates etc. in finance and insurance, and to model time-varying parameter for network problems.
