Measuring chaos and synchronization of chaotic satellite systems using sliding mode control

In this paper, we measure the chaotic behavior for satellite system through the dissipation, equilibrium points, bifurcation diagrams, Poincare section maps, Lyapunov exponents, and Kaplan-Yorke dimension. We observe the qualitative behavior of satellite systems through these tools to justify the chaos in the system. Synchronization for 2 identical satellite systems using slide mode control is presented. We estimate the equilibrium points of chaotic satellite system. At each equilibrium point, we obtain the eigenvalues of Jacobian matrix of satellite system and verify the unstable region. We calculate Kaplan-Yorke dimension, ie, D-KY=2.1915, which ensures the strange behavior of the system. The qualitative and simulated results are in an excellent agreement.