Application of Uncertain Nonlinear Systems Partial State Variables to Synchronization Control for Rössler Systems

Partial state variables stabilization control of uncertain nonlinear systems is developed for chaos systems synchronization control. Response systems are constructed for uncertain Rössler systems. In order to make response systems track the drive systems asymptotically stable, error systems with uncertain and nonlinear factors are designed. Using partial state stability theory of nonlinear systems and adaptive control method, a Lyapunov function is constructed for the uncertain nonlinear error systems, and partial state variables stabilization controller and adaptive regulators are designed. Employing Lyapunov stability theory, we prove that our controller can guarantee the uniformly ultimate boundedness of the solution of the closedloop system, and make the tracking error arbitrarily small for uncertain parameters. Numerical simulation results illustrate the effectiveness of the proposed controllers and adaptive regulators.