Linear Matrix Inequalities: Stability and Optimization

This lecture covers stability analysis for linear time-varying and switched systems using Lyapunov theory, focusing on stability concepts for LTV systems and discrete-time linear switched systems. It introduces the concept of Linear Matrix Inequalities (LMIs) and their role in stability tests and optimization problems. The instructor explains how to define stability for LTV systems and switched systems, emphasizing the importance of Lyapunov theory in casting stability tests into optimization problems. The lecture also discusses the conditions for exponential stability in switched systems and presents the theorem for determining exponential stability using a common Lyapunov function. Additionally, it provides a brief introduction to LMIs, their significance in control theory, and their application in optimization and feasibility problems.