TY - GEN

T1 - Polynomial Lyapunov functions for exponential stability of nonlinear systems on bounded regions

AU - Peet, Matthew M.

AU - Bliman, Pierre Alexandre J.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - This paper presents a proof that the use of polynomial Lyapunov functions is not conservative for studying exponential stability properties of nonlinear ordinary differential equations on bounded regions. The main result implies that if there exists an n-times continuously differentiable Lyapunov function which proves exponential decay on a bounded subset of R-n, then there exists a polynomial Lyapunov function which proves that same rate of decay on the same region. Our investigation is motivated by the use of semidefinite programming to construct polynomial Lyapunov functions for delayed and nonlinear systems of differential equations.

AB - This paper presents a proof that the use of polynomial Lyapunov functions is not conservative for studying exponential stability properties of nonlinear ordinary differential equations on bounded regions. The main result implies that if there exists an n-times continuously differentiable Lyapunov function which proves exponential decay on a bounded subset of R-n, then there exists a polynomial Lyapunov function which proves that same rate of decay on the same region. Our investigation is motivated by the use of semidefinite programming to construct polynomial Lyapunov functions for delayed and nonlinear systems of differential equations.

KW - Lyapunov methods

KW - Nonlinear system control

KW - Stability of NL systems

UR - http://www.scopus.com/inward/record.url?scp=79961017828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79961017828&partnerID=8YFLogxK

U2 - 10.3182/20080706-5-KR-1001.2875

DO - 10.3182/20080706-5-KR-1001.2875

M3 - Conference contribution

AN - SCOPUS:79961017828

SN - 9783902661005

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

BT - Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC

T2 - 17th World Congress, International Federation of Automatic Control, IFAC

Y2 - 6 July 2008 through 11 July 2008

ER -