Analysis and Synthesis of Feedback Systems:Quadratic Functions and LMIs
3.1.1 Description of feedback loop
This chapter starts by addressing the analysis of feedback loops with saturation. In particular, it develops tools for verifying internal stability and quantifying L2 external stability for the well-posed feedback interconnection of a linear system with a saturation nonlinearity. Such a system is depicted in Figure 3.1 and has state-space representation
It is more convenient for analysis and synthesis purposes to express this system in terms of the deadzone nonlinearity q = u — sat(u) as shown in ...