Absolute stability, absolute stabilization and structured dissipativity

In this chapter, we revisit the classical Lur’e-Postnikov approach to the stability of nonlinear control systems. The problems considered in this chapter include the problem of absolute stability and also its extensions such as the problem of absolute stabilization and the problem of structured dissipativity. As in previous chapters of this book, the approach taken here is to convert the problem under consideration into an equivalent H∞ control problem. Such a conversion is accomplished by making use of the corresponding S-procedure theorem.