Homogeneous Lyapunov functions for polynomial systems: a Tensor product approach

Bouzaouache, Hajer; Naceur, B.B.

doi:10.1109/icca.2007.4376694

Cited by 7 publications

(2 citation statements)

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“…But in these investigations the homogeneity plays an important role. For instance, in [3][4][5] the system considered is homogeneous; in [1,3] the Lyapunov function is homogeneous; in [2] the feedback is homogeneous; in [6] the derivative is homogeneous, etc. Obviously, homogeneity brings restriction and/or conservative to the application of the methods presented above.…”

Section: Introductionmentioning

confidence: 99%

“…Grun [4] showed that for any asymptotically controllable homogeneous system in Euclidian space, there exists a homogeneous control Lyapunov function and a homogeneous, possibly discontinuous state feedback law stabilizing the corresponding sampled closed loop system. The Kronecker product is used for non-quadratic stability analysis and sufficient conditions for global asymptotic stability of polynomial systems are obtained in terms of LMI feasibility tests for the existence of homogeneous Lyapunov functions of even degree [1] . But in these investigations the homogeneity plays an important role.…”

Section: Introductionmentioning

confidence: 99%

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Stability of Switched Polynomial Systems

Qiao

et al. 2008

J Syst Sci Complex

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This paper investigates the stability of (switched) polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a (switched) polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.

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