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.

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