Dynamical Stability Analysis And Control Design For Several Class Of Nonlinear Systems

The stabilization and control design of the nonlinear system is one of the hot topics in recent years. A lot of results have been applied to engineering sciences and social sciences. Especially After the fractional calculus has been utilized to describe the performance of the dynamics, the fractional-order system, including fractional-order nonlinear system, has been extensively studied. This dissertation considers the stability and stabilization analysis for integer-order(IO) nonlinear system, including the robust stability analysis for the uncertain integer-order nonlinear system. Furthermore, it investigates the problem of stability and stabilization for fractional-order(FO) nonlinear system, including control and synchronization of fractional-order chaotic systems. Especially, this dissertation proposes the fractional-order sliding mode control and sliding-mode extremum seeking control design for the problem of maximum power point tracking for the photovoltage(PV) and minimum energy usage tracking for the cognitive lighting system. This dissertation is organized as follows:(I) The problem of robust asymptotical stability for a class of integer-order(IO)nonlinear uncertain mixed neutral and Lur’e with time-varying delays is studied. The proposed method is based on Lyapunov theory, a delay-dependent criterion for asymptotic stability is established. It is reduced the conservativeness for this class nonlinear system.(II) The problem of master-slave synchronization for integer-order chaotic Lur’e systems is investigated. The PD controller is employed to synchronization for the class systems, in order to ensure complete synchronization.(III) A PD controller is designed to guarantee the robust H∞stability in a class of uncertain nonlinear Lurie systems. Based on Lyapunov functions and convex representation of sector and slope bounds, the parameters of the controller is decided by applying the linear matrix inequality(LMI) technology. The PD controller is applied to guarantee the system H∞stability.(IV) The design of an adaptive sliding mode controller(ASMC) for chaos control of a class of FO chaotic systems is considered. The controller is designed to achieve to the switching surface in finite time, and guarantee asymptotical stability of the fractionalorder sliding dynamics system. The uncertainty and external disturbance is considered.Appropriate adaptive laws can reduce chattering phenomenon.(V) An ASMC is designed to achieve to master-slave synchronization of two different FO chaotic systems. Appropriate adaptive laws are used to tackle the unknown parameters, uncertainties and external disturbances. The ASMC is built to ensure synchronization of two different fractional-order systems and the finite-time convergence of the sliding motion.(VI) The problem of robust stability for a class of uncertain fractional-order nonlinear systems is considered by designing a sliding mode controller. A central analysis method is enabled by utilized a fundamental boundedness lemma. A robust stability criterion for the systems under the sliding mode controller is given in terms of LMI.(VII) A sliding-mode based extremum seeking controller(SM-ESC) is designed for optimization of nonlinear systems. This controller involving a tanh function can guarantee that the output reaches the small vicinity of the optimal(maximum or minimum)operational point. The controller is shown to have a possibility to have a faster and higher accuracy control performance. The control system is proven to be stability, even if the nonlinear system perturbed by varying environment. The SM-ESC is applied to PV system and achieves to MPPT of the PV.(VIII) In order to save lighting electricity in the hybrid lighting, a minimum point tracking algorithm is developed to achieve the minimized energy usage. An adaptive minimum energy cognitive lighting control prototype is proposed, designed and built. A PID control law is applied to maintain an given level of illumination. Then, an FO SMESC is employed to minimize energy usage in the lights.