INTRODUCTION TO ^ AND LFTS
The chapter is organized as follows. In the first section, simple examples illustrate how to transform a specific control problem into the standard interconnection structure. This qualitative presentation will be completed by a technical presentation of the associated methods in chapter 3. These techniques will be moreover applied to the aeronautical examples in chapter 4.
The s. s.v. is then introduced in a qualitative way in the second section. More precisely, we first focus on the problem of robust stability inside the left half plane. The s. s.v. provides a solution to this problem, first in the context of parametric uncertainties, and then in the general context of mixed uncertainties (i. e. parametric uncertainties and neglected dynamics). The third section considers robust performance problems, and shows that the s. s.v. provides a general framework for analyzing the robustness properties of a closed loop subject to model uncertainties.
The Ц framework is finally introduced in a formal way in the last section. The (skewed) s. s.v. is first defined. The Main Loop Theorem, which plays a key role in the ц approach, is then introduced, before being interpreted in a qualitative way in the specific context of robust performance problems. Some difficulties of the ц approach are finally briefly indicated, and especially the need to compute bounds of the s. s.v. instead of the exact value. These difficulties will be further studied in the next chapters.