This book puts forward the concept of a virtual equivalent system (VES) based on theoretical analysis and simulation results. The new concept will facilitate the development of a uniï¬ed framework for analyzing the stability and convergence of self-tuning control (STC) systems, and potentially, of all adaptive control systems. The book then shows that a time-varying STC system can be converted into a time-invariant system using a certain nonlinear compensation signal, which reduces the complexity and diï¬culty of stability and convergence analysis. In closing, the VES concept and methodology are used to assess the stability of multiple model adaptive control (MMAC) systems and T-S model-based fuzzy control systems.