In this paper we adopt a new technique combined with operator theorem to analysis linear time-varying system. This make us solve the robust control problems of linear time-varying system more easily. Also, we can apply this method to the problems of linear time-invarying system. First, we construct the operator we want to use, then apply it to the linear time-varying system. Moreover, we can apply this method to the structure singular value problem of robust control, and the result is similar with the linear time-invarying system. Then , we construct the standard control problem , and adopt linear matrix in- equality to get suboptimal controller to satisfy the robust performance we need. Finally,we use numerical method to discuss it.

Solar Wireless Networked Control Systems (SWNCS) are a style of distributed control systems where sensors, actuators, and controllers are interconnected via a wireless communication network. This system setup has the benefit of low cost, flexibility, low weight, no wiring and simplicity of system diagnoses and maintenance. However, it also unavoidably calls some wireless network time delays and packet dropout into the design procedure. Solar lighting system offers a clean environment, therefore able to continue for a long period. SWNCS also offers multi Service infrastructure solution for both developed and undeveloped countries. The system provides wireless controller lighting, wireless communications network (WI-FI/WIMAX), CCTV surveillance, and wireless sensor for weather measurement which are all powered by solar energy.

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A methodology of designing an adaptive sliding mode controller for a class of nonlinear systems with matched and mismatched perturbations is proposed in this thesis. A specific designed sliding surface function is presented first, whose coefficients are determined by using Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. Without requiring the upper bounds of matched perturbations, the controller with adaptive mechanisms embedded is also designed by using Lyapunov stability theorem. The proposed control scheme not only can drive the trajectories of the controlled systems reach sliding surface in finite time, but also is able to suppress the mismatched perturbations when the controlled systems are in the sliding mode, and achieve asymptotic stability. In addition, the proposed control scheme can be directly applied to a class of underactuated systems. A numerical example and a practical experiment are given for demonstrating the feasibility of the proposed control scheme.

This thesis concerns stability analysis and robust H¡Û performance analysis for discrete-time systems with interval time-varying delay; moreover, the results are extended to the systems with norm-bounded uncertainties. By defining a novel Lyapunov functional and combining delay partition methods to improve the results in existing literature, we obtain a less conservative linear matrix inequality condition to guarantee the asymptotic stability for the discrete-time systems. There are examples to illustrate the advantage of our method in every chapter.

In this dissertation, the stabilization problem and observer-based control of neutral systems are investigated. Firstly, the Lyapunov functional theory is used to guarantee the stability of the system under consideration. The delay-dependent and the delay-independent stabilization criteria are proposed to guarantee asymptotic stability for the neutral systems via linear control. Linear matrix inequality (LMI) approach is used to design the observer and the controller. Secondly, by using the same techniques, we will provide an observer-based controller design method. The delay-dependent and the delay-independent stabilization criteria are proposed to guarantee asymptotic stability for the neutral systems with multiple time delays. Finally, a guaranteed-cost observer-based control for the neutral systems is considered. The analysis is also based on Lyapunov functional so as to establish an upper bound on the closed-loop value of a quadratic cost function. Delay-independent stabilization criterion is proposed to guarantee asymptotic stability for the neutral systems via linear control. By using the LMI approach, we will provide a criterion to design the observer gain and the controller gain simultaneously. Some examples and computer simulation results will also be provided to illustrate our main results.

In this dissertation, we will investigate the global stability for some uncertain neural networks with multiple time-varying delays. These well-known neural networks include delayed cellular neural networks (DCNNs), delayed bidirectional associative memory neural networks (DBAMNNs), and delayed Cohen-Grossberg neural networks (DCGNNs). Delay-dependent and delay-independent criteria will be proposed to guarantee the robust stability of these uncertain delayed neural networks via linear matrix inequality (LMI) approach. Three types of uncertainties on feedback and delayed feedback matrices in these uncertain delayed neural networks will be considered in this study, namely uncertainties with structured perturbation, norm-bounded unstructured perturbation, and interval perturbation. Some numerical examples will be given to illustrate the effectiveness of our results. Some comparisions are made to show that our results are better than some results in recent literature.

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State dependent Riccati equation (SDRE) plays an important role in nonlinear controller design. For autonomous nonlinear systems that can be expressed in linear form with state-dependent coefficients (SDC), SDRE-based controllers guarantee local asymptotic stability of the closed-loop system, under pointwise stabilizability and detectability conditions. Moreover, the optimal control for a quadratic cost function, when it exists, corresponds to an SDRE-based control design for a specific SDC parameterization of the associated nonlinear system. Unfortunately, the implementation of the SDRE-based controllers is computationally expensive. Various techniques have been developed for solving the SDRE, which are either computationally expensive or lack acceptable precision. In this dissertation, a modified state-dependent differential Riccati equation (MSDDRE) is proposed for approximating the solution of the SDRE, which is easy to implement with moderate computation power and its solution can be made arbitrarily close to that of the SDRE. Therefore, it can be used for real-time implementation of near-optimal controllers for nonlinear systems in state-dependent linear form. The proposed technique is then extended to SDRE-based filter design and its application to SDRE-based output feedback control technique. The proposed technique is also extended to state-dependent H-inf; robust control design for a constant noise attenuation bound, when the solution exists. To reduce the design conservativeness, the technique is further extended to state-dependent H-inf; robust control design with adaptive noise attenuation bound, using gain-scheduling technique and linear matrix inequality (LMI) optimization, to approximate H-inf; optimal control with state-dependent noise-attenuation bound. Local asymptotic stability of the closed-loop system is proven for all proposed techniques. Simulation results further confirm the validity of the development and demonstrate the efficiency of the proposed techniques.

In order to reduce the detrimental effects of inter-area oscillations on system stability, it is possible to use Linear Matrix Inequalities (LMIs) to design a multi-objective state feedback. The LMI optimization finds a control law that stabilizes several contingencies simultaneously using a polytopic model of the system. However, the number of cases to be considered is limited by computational complexity which increases the chances of infeasibility. In order to circumvent this problem, this paper presents a method for solving multiple polytopic problems having a common base case. The proposed algorithm determines the necessary polytopic control for a particular contingency and classifies the data as belonging to that polytopic domain. The technique has been tested on an 8-machine, 13 bus, system and has been found to give satisfactory results. / Master of Science