By using Lyapunov stability theorem, a quasi-optimal model reference adaptive control (QOMRAC) scheme is presented in this thesis to stabilize a class of uncertain systems with input nonlinearity. This control scheme contains two main types of controllers. The first type is a linear feedback controller, which is an optimal controller if the controlled systems do not have any perturbations. The second type is an adaptive controller, which is used for adapting the unknown upper bound of perturbation or perturbation estimation error. The property of uniformly ultimately boundness is guaranteed when employing the proposed control scheme, and the effects of each design parameter on the dynamic performance are also analyzed. An example is demonstrated for showing the feasibility of the proposed control scheme.

The objective of this thesis is to solve the trajectory tracking control problems of the mobile manipulators in two stages. In the first stage, a desired velocity input function for a steering system is designed by using Lyapunov stability theorem so that the posture of the mobile manipulator can track the reference trajectory. Further analysis shows that the vehicle of the mobile manipulator will achieve better result of trajectory tracking than the existent methods if the reference trajectory of the vehicle is not assigned to be static condition. In the second stage, the torque controller of the dynamic equations of the mobile manipulator with perturbations and input uncertainty is designed by adaptive variable structure control (AVSC) methodology, so that the actual velocity can track the desired velocity input function designed in the first stage. In addition, this controller with an adaptive mechanism embedded is capable of suppressing the perturbations with unknown upper bound except that from the input channel, and achieve asymptotical stability under certain mild conditions. Finally, an example of a two-link wheeled mobile manipulator is presented to demonstrate the feasibility of the proposed control schemes.

A simple technique of designing a robust discrete-time variable structure output tracking controller for a class of perturbed MIMO linear and nonlinear systems is proposed in this thesis. For linear systems, a model reference scheme is employed. Both an adaptive mechanism and a perturbation estimation process are embedded in the proposed control scheme. The information of the upper bound of the perturbation estimation error is not required due to the usage of adaptive mechanism. It is shown that the dynamics of the controlled systems will be driven into the vicinity of the designed switching surface, therefore the tracking error will be constrained in a small bounded region. Furthermore, the stability of the overall controlled system is guaranteed, and one can increase the tracking accuracy by adjusting the controller's parameters or by employing the perturbation estimation process.

Based on the Lyapunov stability theorem, a methodology of designing robust discrete-time model reference variable structure state tracking controller is proposed in this thesis for a class of multi-input multi-output (MIMO) discrete-time systems. This variable structure controller is composed of three types of controllers. The first one is the feedback control law, which can eliminate the nominal term in the derivative of a Lyapunov function. The second one is the switching control law, which can determine the decreasing rate of the Lyapunov function. The third one is the adaptive control law, which is used to overcome the perturbations. The resultant robust variable structure controllers are capable of driving all the trajectories of tracking errors toward a small bounded region. The information of upper bound of the perturbation, which is not a constant and is dependent on the norm of state variable, is not required beforehand due to some adaptive mechanisms are embedded in the proposed control scheme, and the stability of the overall controlled system is guaranteed. A numerical example and a practical example are given to demonstrate the feasibility of the proposed control scheme.

Two robust control strategies are proposed in this dissertation for a class of multi-input multi-output dynamic systems with matched and mismatched perturbations. First of all, a novel design methodology of switching variables is proposed for solving the regulation problems. A serial state transformations are needed in order to design pseudo feedback gains and adaptive mechanisms. By utilizing the pseudo control input gain embedded in each of the switching variable, the proposed controller can not only suppress the mismatched perturbations when the controlled systems are in the sliding mode, but also attain locally asymptotic stability. The design of a robust output tracking controller is presented next for solving the tracking problems. Without utilizing the information of state variable, the proposed output feedback tracking controllers are capable of driving the state tracking errors into a small bounded region whose size can be adjusted through the designed parameters, and guarantee the stability of controlled systems. These two robust control schemes are designed by means of the variable structure control technique with sliding mode and Lyapunov stability theorem. Each controller contains three parts. The first part is for eliminating measurable feedback signals. The second part is used for adjusting the convergent rate of state variables (or tracking errors) of the controlled system. The third part is an adaptive control mechanism, which is to adapt some unknown constants of the least upper bounds of perturbations, so that the knowledge of the least upper bounds of matched and mismatched perturbations are not required. Several numerical examples and an application of controlling aircraft's velocity are demonstrated for showing the feasibility of the proposed control methodologies.

Three robust tracking control design strategies are proposed in this dissertation for different classes of nonlinear MIMO dynamic systems with mismatched perturbations. The first controller design method is proposed for a class of nonlinear MIMO dynamic systems in canonical form. The second design procedure of controller is for the nonlinear MIMO dynamic systems without canonical form. A decentralized controller is presented in the last for perturbed large-scale systems with time-varying delay interconnections, where the knowledge of the exact function of time-delay is not required. These robust tracking controllers with a perturbation estimating scheme and an adaptive control mechanism embedded are designed by means of the variable structure control technique and Lyapunov stability theorem. The adaptive control mechanism is used to adapt the unknown upper-bound of perturbation estimation error, so that the knowledge of upper-bounds of perturbation as well as perturbation estimation error is not required. The chattering phenomenon is effectively alleviated, for the gain of the proposed controllers, which needs only to overcome the perturbation estimation error, is in general smaller than those of the traditional sliding mode controllers. Furthermore, the stability of the overall controlled systems is proved, and the desired tracking accuracy can be achieved by adjusting the design parameters of the proposed controller schemes. A numerical example for each controller's design is provided for demonstrating the feasibility of the proposed control schemes.

Abstract In this dissertation, four variable structure controllers are proposed for four different class of systems subjected to uncertainties and time varying delays respectively. In most cases, the variable structure control is incorporated with an adaptive law to drive the tracking error between the desired model and the controlled plant to zero. By using the Lyapunov stability theorem, the adaptive law is utilized for adapting the unknown upper bounds of the lumped perturbations so that the objective of asymptotical stability is achieved, and the variable structure control scheme is used for enhancing the robustness of stability of the controlled systems. Once the system enters the sliding region, the dynamics of controlled systems are insensitive to matching perturbations. It also shows that the proposed methodologies ensure the property of the globally uniformly ultimate boundness for the overall controlled system. Finally, four numerical examples are given for demonstrating the feasibility of the proposed control schemes.

Based on the Lyapunov stability theorem, an adaptive output feedback controller is proposed in this thesis for a class of multi-input multi-output (MIMO) dynamic systems with time-varying delay and disturbances. With an adaptive mechanism embeded in the proposed control scheme, the controller will automatically adapt the unknown upper bound of perturbation, so that the information of upper bounded of perturbations is not required. Once the controlled system reaches the switching hyperplane, not only the dynamics of system can be stabilized, but also the state trajectories can be driven into a small bounded region whose size can be adjusted through the design parameter. Two numerical examples are given for demonstrating the feasibility of the proposed control scheme.

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Sliding mode control (SMC) has been successfully applied to many practical control problems due to its attractive features such as invariance to matched uncertainties. The characteristic feature of a continuous-time SMC system is that sliding mode occurs on a prescribed manifold, where switching control is employed to maintain the state on the surface. When a sliding mode is realized, the system exhibits some superior robustness properties with respect to external matched uncertainties. However, the realization of the ideal sliding mode requires switching with an infinite frequency. Control algorithms are now commonly implemented in digital electronics due to the increasingly affordable microprocessor hardware although the essential conceptual framework of the feedback design still remains to be in the continuous-time domain. Discrete sliding mode control has been extensively studied to address some basic questions associated with the sliding mode control of discrete-time systems with relatively low switching frequencies. However, the complex dynamical behaviours due to discretization in continuous-time SMC systems have not yet been fully explored. In this thesis, the discretization behaviours of SMC systems are investigated. In particular, one of the most frequently used discretization schemes for digital controller implementation, the zero-order-holder discretization, is studied. First, single-input SMC systems are discretized, stability and boundary conditions of the digitized SMC systems are derived. Furthermore, some inherent dynamical properties such as periodic phenomenon, of the discretized SMC systems are studied. We also explored the discretization behaviours of the disturbed SMC systems. Their steady-state behaviours are discussed using a symbolic dynamics approach under the constant and periodic matched uncertainties. Next, discretized high-order SMC systems and sliding mode based observers are explored using the same analysis method. At last, the thesis investigates discretization effects on the SMC systems with multiple inputs. Some conditions are first derived for ensuring the