Title :
A negative result on piecewise quadratic Lyapunov functions for decay rate analysis
Author :
Spångéus, Per ; Jirstrand, Mats
Author_Institution :
Dept. of Electr. Eng., Linkoping Univ., Sweden
Abstract :
In recent years, the advent of efficient methods for solving linear matrix inequality (LMI) problems has yielded a new interesting class of Lyapunov functions, the piecewise quadratic Lyapunov functions, subject to efficient computation. This class has shown promise, e.g. in the stability analysis of hybrid systems. In this paper, we describe one example that we have analyzed in order to investigate how LMI methods and piecewise quadratic Lyapunov functions can be used to iteratively synthesize a switched control law in order to obtain an improved decay rate. The example shows that piecewise quadratic Lyapunov functions are not sufficient to analyze the decay rate of a piecewise affine system, given that the partitioning used in the Lyapunov function is the same as in the piecewise affine system. As noted in other performance analysis examples, a finer partitioning is needed
Keywords :
Lyapunov matrix equations; control system analysis; control system synthesis; functions; performance index; piecewise polynomial techniques; stability; decay rate analysis; efficient computation; hybrid systems; iterative synthesis; linear matrix inequality problems; partitioning; performance analysis; piecewise affine system; piecewise quadratic Lyapunov functions; stability analysis; switched control law; Clocks; Control system synthesis; Linear systems; Lyapunov method; Performance analysis; Q measurement; Roentgenium; Stability analysis; State-space methods; Switches;
Conference_Titel :
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5250-5
DOI :
10.1109/CDC.1999.831266