×

Robust exponential converge controller design for a unified chaotic system with structured uncertainties via LMI. (English) Zbl 1191.93046

Summary: This paper focuses on the chaos control problem of the unified chaotic systems with structured uncertainties. Applying Schur-complement and some matrix manipulation techniques, the controlled uncertain unified chaotic system is then transformed into the Linear Matrix Inequality (LMI) form. Based on Lyapunov stability theory and LMI formulation, a simple linear feedback control law is obtained to enforce the prespecified exponential decay dynamics of the uncertain unified chaotic system. Numerical results validate the effectiveness of the proposed robust control scheme.

MSC:

93B52 Feedback control
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
93B35 Sensitivity (robustness)
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises 24 pp xxii+753– (1998)
[2] DOI: 10.1103/PhysRevLett.64.1196 · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[3] DOI: 10.1142/S0218127499001024 · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[4] DOI: 10.1142/S0218127402004620 · Zbl 1063.34510 · doi:10.1142/S0218127402004620
[5] DOI: 10.1142/S021812740200631X · Zbl 1043.37026 · doi:10.1142/S021812740200631X
[6] DOI: 10.1007/BF02169423 · Zbl 0747.93071 · doi:10.1007/BF02169423
[7] International Series of Numerical Mathematics 97, in: Controllability of Lorenz equation pp 257– (1991)
[8] DOI: 10.1007/BF02115741 · Zbl 0792.93041 · doi:10.1007/BF02115741
[9] DOI: 10.1007/BF01985075 · Zbl 0825.93547 · doi:10.1007/BF01985075
[10] DOI: 10.1103/PhysRevLett.75.2952 · doi:10.1103/PhysRevLett.75.2952
[11] DOI: 10.1016/j.chaos.2004.02.004 · Zbl 1060.93536 · doi:10.1016/j.chaos.2004.02.004
[12] DOI: 10.1016/S0960-0779(02)00203-5 · Zbl 1042.93510 · doi:10.1016/S0960-0779(02)00203-5
[13] DOI: 10.1016/j.chaos.2003.12.019 · Zbl 1049.93040 · doi:10.1016/j.chaos.2003.12.019
[14] DOI: 10.1016/j.physleta.2009.06.006 · Zbl 1233.93047 · doi:10.1016/j.physleta.2009.06.006
[15] SIAM Studies in Applied Mathematics 15 pp xii+193– (1994)
[16] DOI: 10.1109/TAC.2003.812784 · Zbl 1364.93654 · doi:10.1109/TAC.2003.812784
[17] DOI: 10.1109/9.486646 · Zbl 0854.93113 · doi:10.1109/9.486646
[18] DOI: 10.1016/j.automatica.2006.09.011 · Zbl 1137.93044 · doi:10.1016/j.automatica.2006.09.011
[19] DOI: 10.1016/j.chaos.2007.10.043 · Zbl 1198.34155 · doi:10.1016/j.chaos.2007.10.043
[20] DOI: 10.1142/S0218127406015179 · Zbl 1097.94038 · doi:10.1142/S0218127406015179
[21] DOI: 10.1016/j.automatica.2004.06.001 · Zbl 1162.93353 · doi:10.1016/j.automatica.2004.06.001
[22] DOI: 10.1109/TCSI.2005.854412 · doi:10.1109/TCSI.2005.854412
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.