Based on the Lyapunov stability theorem, two different variable structure controllers are proposed in this thesis for two different classes of multi-variable descriptor systems subject to matched nonlinear perturbations. The integral variable structure controller is proposed first for solving the stabilization problems, and model reference variable structure controller is the second for solving the state tracking problems. Both proposed control schemes can guarantee the trajectories of the controlled systems to lie in the sliding surface from initial time, so that the properties of regularity, impulse free, and stability can be obtained. Two numerical examples are given for demonstrating the feasibility of the proposed control schemes.

Based on the Lyapunov stability theorem, a methodology of designing an nth order adaptive integral variable structure derivative estimator (AIVSDE) is proposed in this thesis. The proposed derivative estimator not only is an improved version of the existing AIVSDE, but also can be used to estimate the nth derivative of a smooth signal which has continuous and bounded derivatives up to n+1. Analysis results show that adjusting some of the parameters can facilitate the derivative estimation of signals with higher frequency noise. The adaptive algorithm is incorporated in the estimation scheme for tracking the unknown upper bounded of the input signal as well as their's derivatives. The stability of the proposed derivative estimator is guaranteed, and the comparison between recently proposed derivative estimator of high-order sliding mode control and AIVSDE is also demonstrated.

Two application applications of Fuzzy Logic to improve the performance of two controllers are presented. The first application takes a Sliding Mode Controller designed for chemical process to reject disturbances. A fuzzy element is added to the sliding surface to improve the controller performance when set point change affects the control loop; especially for process showing highly nonlinear behavior. This fuzzy element, , is calculated by means of a set of fuzzy rules designed based on expert knowledge and experience. The addition of improved the controller response because accelerate or smooth the controller as the control loop requires. The Fuzzy Sliding Mode Controller (FSMCr) is a completely general controller. The FSMCr was tested with two models of nonlinear process: mixing tank and neutralization reactor. In both cases the FSMCr improves the performance shown for other control strategies, as the industrial PID, the conventional Sliding Mode Control and the Stan dard Fuzzy Logic Controller. The second part of this research presents a new way to implement the Dynamic Matrix Control Algorithm (DMC). A Parametric structure of DMC (PDMC) control algorithm is proposed, allowing to the controller to adapt to process nonlinearities. For a standard DMC a process model is used to calculate de controller response. This model is a matrix calculated from the dynamic response of the process at open loop. In this case the process parameters are imbibed into the matrix. The parametric structure isolates the process parameters allowing adjust the model as the nonlinear process changes its behavior. A Fuzzy supervisor was developed to detect changes in the process and send taht [sic]information to the PDMCr. The modeling error and other parameters related were used to estimate those changes. Some equations were developed to calculate the PDMCr tuning parameter,lambda, as a function of the process parameters. The performance of PDMCr was tested using to model of nonlinear process and compare with the standard DMC; in most the cases PDMCr presents less oscillations and tracks with less error the set point. Both control strategies presented in this research can be implemented into industrial applications easily.

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