Composite homogeneous parameter dependent quadratic Lyapunov functions

This paper presents a new type of Lyapunov function which is called composite homogeneous parameter dependent quadratic Lyapunov function. By using this function, a condition is derived in terms of an auxiliary feedback matrix for determining if a given convex hull is an estimation of attractive reg...

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Bibliographic Details
Published in2017 36th Chinese Control Conference (CCC) pp. 100 - 105
Main Authors Guochen Pang, Zhong Xiang, Feng Zhao
Format Conference Proceeding
LanguageEnglish
Published Technical Committee on Control Theory, CAA 01.07.2017
Subjects
Actuators
Asymptotic stability
Contractively invariance
Domain of attraction
Electronic mail
Ellipsoids
Estimation
Homogeneous polynomial functions
Level set
Lyapunov methods
Quadratic Lyapunov functions
Saturating actuator
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Summary:This paper presents a new type of Lyapunov function which is called composite homogeneous parameter dependent quadratic Lyapunov function. By using this function, a condition is derived in terms of an auxiliary feedback matrix for determining if a given convex hull is an estimation of attractive region for a system under a saturated linear feedback. Most of the cases, the shape of attractive region is irregular. So, using simple ellipsoid to estimate the attractive region will bring conservativeness. However, if we use the complex polyhedron to estimate attractive region, the polyhedron is obviously more closer to attractive region than the simple ellipsoid. Along this direction, we get this polyhedron by constructing the level set of composite homogeneous parameter dependent quadratic Lyapunov function. Simulation results show the features of the proposed design the composite homogeneous parameter dependent quadratic Lyapunov function brings about.
ISSN:2161-2927
DOI:10.23919/ChiCC.2017.8027328