Ohta, Yuzo (Kobe Univ.), Mori, Kohei (Kobe Univ.)

On the Construction of Piecewise Linear Lyapunov Functions: Further Improved Results

Scheduled for presentation during the Regular Session "Stability I" (WeA13), Wednesday, July 26, 2006, 11:15−11:40, Room 101

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 24, 2024

Abstract

In this paper, the issue of constructing piecewise linear Lyapunov functions (PLLF) for stability analysis of polytopic uncertain linear systems is considered. Candidates of PLLF are parametrized by hyperplanes, which intersect the given region, and stability conditions are formulated as Linear Programming Problems (LPs) in terms of the parameters inserted by the hyperplanes. If the optimal value of the LP is negative, then PLLF is constructed by using the optimal solution of it. When the optimal value of the LP is nonnegative, the candidate of PLLF is modified by adding new dividing hyperplanes to increase the freedom and a new LP is formulated corresponding to the new PLLF candidate. A necessary condition and sufficient conditions so that the optimal value of the new LP strictly decreases by adding a dividing hyperplane were derived. In this paper, a necessary and sufficient condition for the strictly decrease of the optimal value of the new LP is derived. An example is used to illustrate the obtained result.