Stabilizing the unstable periodic orbits of a chaotic system using adaptive time-delayed state feedback

Stabilizing the unstable periodic orbits of a chaotic system using model independent adaptive time-delayed controller

“…If moreover we can choose matrices P , R and K such that Q in (14) is negative definite, then we can deduce that η = 0 is a stable equilibrium of (19) which implies that η(t) ∈ L ∞ . From (19) and by the choice (21), we obviously haveη(t) ∈ L ∞ .…”

“…From (19) and by the choice (21), we obviously haveη(t) ∈ L ∞ . Hence, η(t) is a continuous function.…”

“…Should we apply the noisy controller to the system, then we obtain a similar expression to (19) given bẏ…”

“…The second, uses the control strategy to achieve synchronization between two identical or different chaotic systems [9][10][11][12][13]. The third, is the most important when it comes to the control of chaotic systems, and concerns the stabilization of unstable periodic orbits embedded in the chaotic attractor [14][15][16][17][18][19].…”