Abstract
This chapter describes the analysis and synthesis of feedback systems, with particular emphasis on quadratic functions and linear matrix inequalities (LMIs). It first considers the analysis of feedback loops with saturation, with the goal of developing tools for verifying internal stability and quantifying L₂ external stability for the feedback interconnection of a linear system with a saturation nonlinearity. It then discusses quadratic functions and semidefinite matrices, along with the use of quadratic functions to analyze unconstrained feedback systems. It also demonstrates how the LMI feasibility and eigenvalue problems can be solved efficiently using modern numerical software packages. Furthermore, it looks at the global vs. regional analysis of unconstrained feedback systems. A few examples of nonlinear gain computation are provided to illustrate the use of the LMIs. The chapter concludes by explaining regional synthesis in feedback loops with saturation based on the LMIs.
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