FTS Analysis Via PQLFs

Abstract

This chapter deals with the FTS analysis for CT-LTV systems when the initial and trajectory domains are piecewise quadratic. The approaches presented in the previous chapters of the book make use of quadratic Lyapunov functions to perform the FTS analysis and control of a given system. This is consistent with the fact that the initial and trajectory domains have been assumed to be ellipsoidal. The main contribution of this chapter is to consider a more general class of Lyapunov functions, namely the family of Piecewise Quadratic Lyapunov Functions (PQLFs). In particular, a novel sufficient condition for the FTS of CT-LTV systems, based on the PQLFs approach, is provided; then a procedure is proposed to convert such a condition into a computationally tractable problem. The numerical examples included at the end of the chapter are divided into three parts: first, we introduce a comparison with the other results presented in this book when ellipsoidal initial and trajectory domains are considered; then we present an example in which the domains have different structures, that is, a polytopic initial domain and an ellipsoidal trajectory domain; finally, the general case in which both the domains are polytopic is discussed in the third example. In the last two examples, the conditions developed in Chap. 2 can only be applied with added conservativeness due to the necessity of approximating the polytopic domains by ellipsoidal domains.