Hybrid singularly perturbed systems (SPSs) with time delay are considered and exponential stability of these systems is investigated. This work mainly covers switched and impulsive switched delay SPSs . Multiple Lyapunov functions technique as a tool is applied to these systems. Dwell and average dwell time approaches are used to organize the switching between subsystems (modes) so that the hybrid system is stable. Systems with all stable modes are first discussed and, after developing lemmas to ensure existence of growth rates of unstable modes, these systems are then extended to include, in addition, unstable modes. Sufficient conditions showing that impulses contribute to yield stability properties of impulsive switched systems that consist of all unstable subsystems are also established. A number of illustrative examples are presented to help motivate the study of these systems.

Motivated by ongoing research into automating radiotherapy, this thesis is concerned with linear feedback control and estimation problems where only a delayed output signal is measurable. Various discrete-time performance limitations are derived using tools from model-matching theory as well as the early $H_\infty$ literature. It is shown that there exist performance limitations for both one-degree-of-freedom control and estimation problems, but the nature of the limitations differs depending on whether the plant is stable or unstable. Some continuous-time performance limitations are also found, with more complete results in the case where the plant is unstable. Extensions of the various performance limitation to two-degree-of-freedom control are also studied.

Hybrid singularly perturbed systems (SPSs) with time delay are considered and exponential stability of these systems is investigated. This work mainly covers switched and impulsive switched delay SPSs . Multiple Lyapunov functions technique as a tool is applied to these systems. Dwell and average dwell time approaches are used to organize the switching between subsystems (modes) so that the hybrid system is stable. Systems with all stable modes are first discussed and, after developing lemmas to ensure existence of growth rates of unstable modes, these systems are then extended to include, in addition, unstable modes. Sufficient conditions showing that impulses contribute to yield stability properties of impulsive switched systems that consist of all unstable subsystems are also established. A number of illustrative examples are presented to help motivate the study of these systems.

Motivated by ongoing research into automating radiotherapy, this thesis is concerned with linear feedback control and estimation problems where only a delayed output signal is measurable. Various discrete-time performance limitations are derived using tools from model-matching theory as well as the early $H_\infty$ literature. It is shown that there exist performance limitations for both one-degree-of-freedom control and estimation problems, but the nature of the limitations differs depending on whether the plant is stable or unstable. Some continuous-time performance limitations are also found, with more complete results in the case where the plant is unstable. Extensions of the various performance limitation to two-degree-of-freedom control are also studied.

The main purpose of this thesis is to estimate the direct path in dense multipath Ultra Wide-Band (UWB) environment. The time-of-arrival (ToA) estimation algorithm used is based on Generalized Maximum-Likelihood (GML) algorithm. Nevertheless, GML algorithm is so time-consuming that the results usually take a very long period of time, and sometimes fail to converge. Hence, the schemes that would improve the algorithm are investigated. In the schemes, the search was executed in sequential form. Two threshold parameters are to be determined¡Xone is about the arrival time of the estimation path while the other is the fading amplitude of the estimation path. The thresholds are determined in order to terminate the sequential algorithm. The determination of thresholds is based on error analysis, including the probability of error and root-mean-square error. The analysis of the probability of error is subject to the probability of false alarm and the probability of miss. However, a trade-off problem on the probability of false alarm and the probability of miss exists in the process of determining thresholds. The thresholds are determined according to the requirement of the probability of error. We propose an improvement scheme for determining the two thresholds. In the proposed scheme, candidate pairs are evaluated within an appropriate range. The root-mean-square error value for each pair of thresholds is calculated. The smallest error, corresponding to the desired thresholds, is chosen for use in ToA estimation. From the simulation results, it is seen that, when SNR falls between -4dB and 16dB, the improvement proposed scheme results has the smaller estimation error.

In this thesis, an algorithm based on frequency-space domain MUSIC method is presented for estimating the propagation delay of a wireless multipath channel.For indoor geolocation systems, the time-of-arrival (TOA) is the most popular technique for accurate positioning system. The basic idea in TOA-based techniques is to accurately estimate the propagation delay of the radio signal arriving from the direct line-of-sight (DLOS) path. However, dense multipath environments may cause unresolved paths, and yield an error in the estimation of the DLOS path. UWB (Ultra-wideband) technology provides an excellent means for wireless positioning due to its high resolution capability in the time domain. Its ability to resolving multipath components makes it possible to obtain accurate location estimates. In this thesis, we investigate the use of UWB signals in positioning and combine frequency-domain MUSIC algorithm. At the same time, the structure of time-space-time method is studied. In addition, we propose a frequency-space domain MUSIC algorithm, called FSF-MUSIC algorithm, and use the spatial smoothing technique to improve the performance of the algorithm. For a two-multipath case, analysis and simulation results of multipath resolvability and the variance of estimation errors of signal arrival time are discussed.

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.

Two different perturbation estimation methodologies are compared in this thesis. One is time delay method (TDM), the other is sliding mode techniqueli (SMT). When analyzing the TDM, Pade approximation is used to approximate a function with time-delay argument. The comparisons of perturbation estimation accuracy resulted from TDM and SMT both in time domain and frequency domain are addressed, and two numerical examples are also given for demonstration.

A control system in which sensors, actuators, and controllers are interconnected over a communication network is called a networked control system (NCS). Enhanced computational capabilities and bandwidths in the networking technology enabled researchers to develop NCSs to implement distributed control schemes. This dissertation presents a framework for the modeling, design, stability analysis, control, and bandwidth allocation of real-time control over networks. This framework covers key research issues regarding control over networks and can be the guidelines of NCS design. A single actuator ball magnetic-levitation (maglev) system is implemented as a test bed for the real-time control over networks to illustrate and verify the theoretical results of this dissertation. Experimentally verifying the feasibility of Internet-based real-time control is another main objective of this dissertation. First, this dissertation proposes a novel NCS model in which the effects of the networkinduced time delay, data-packet loss, and out-of-order data transmission are all considered. Second, two simple algorithms based on model-estimator and predictor- and timeout-scheme are proposed to compensate for the network-induced time delay and packet loss simultaneously. These algorithms are verified experimentally by the ball maglev test bed. System stability analyses of original and compensated systems are presented. Then, a novel co-design consideration related to real-time control and network communication is also proposed. The working range of the sampling frequency is determined by the analysis of the system stability and network parameters such as time delay, data rate, and data-packet size. The NCS design chart developed in this dissertation can be a useful guideline for choosing the network and control parameters in the design of an NCS. Using a real-time operating system for real-time control over networks is also proposed as one of the main contributions of this dissertation. After a real-time NCS is successfully implemented, advanced control theories such as robust control, optimal control, and adaptive control are applied and formulated to improve the quality of control (QoC) of NCSs. Finally, an optimal dynamic bandwidth management method is proposed to solve the optimal network scheduling and bandwidth allocation problem when NCSs are connected to the same network and are sharing the network resource.

Thesis (M. Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 27-31).