The proliferation and universal adoption of the Internet has made it become the key information transport platform of our time. Congestion occurs when resource demands exceed the capacity, which results in poor performance in the form of low network utilization and high packet loss rate. The goal of congestion control mechanisms is to use the network resources as efficiently as possible. The research work in this thesis is centered on finding ways to address these types of problems and provide guidelines for predicting and controlling network performance, through the use of suitable mathematical tools and control analysis. The first congestion collapse in the Internet was observed in 1980's. To solve the problem, Van Jacobson proposed the Transmission Control Protocol (TCP) congestion control algorithm based on the Additive Increase and Multiplicative Decrease (AIMD) mechanism in 1988. To be effective, a congestion control mechanism must be paired with a congestion detection scheme. To detect and distribute network congestion indicators fairly to all on-going flows, Active Queue Management (AQM), e.g., the Random Early Detection (RED) queue management scheme has been developed to be deployed in the intermediate nodes. The currently dominant AIMD congestion control, coupled with the RED queue in the core network, has been acknowledged as one of the key factors to the overwhelming success of the Internet. In this thesis, the AIMD/RED system, based on the fluid-flow model, is systematically studied. In particular, we concentrate on the system modeling, stability analysis and bounds estimates. We first focus on the stability and fairness analysis of the AIMD/RED system with a single bottleneck. Then, we derive the theoretical estimates for the upper and lower bounds of homogeneous and heterogeneous AIMD/RED systems with feedback delays and further discuss the system performance when it is not asymptotically stable. Last, we develop a general model for a class of multiple-bottleneck networks and discuss the stability properties of such a system. Theoretical and simulation results presented in this thesis provide insights for in-depth understanding of AIME/RED system and help predict and control the system performance for the Internet with higher data rate links multiplexed with heterogeneous flows.

The proliferation and universal adoption of the Internet has made it become the key information transport platform of our time. Congestion occurs when resource demands exceed the capacity, which results in poor performance in the form of low network utilization and high packet loss rate. The goal of congestion control mechanisms is to use the network resources as efficiently as possible. The research work in this thesis is centered on finding ways to address these types of problems and provide guidelines for predicting and controlling network performance, through the use of suitable mathematical tools and control analysis. The first congestion collapse in the Internet was observed in 1980's. To solve the problem, Van Jacobson proposed the Transmission Control Protocol (TCP) congestion control algorithm based on the Additive Increase and Multiplicative Decrease (AIMD) mechanism in 1988. To be effective, a congestion control mechanism must be paired with a congestion detection scheme. To detect and distribute network congestion indicators fairly to all on-going flows, Active Queue Management (AQM), e.g., the Random Early Detection (RED) queue management scheme has been developed to be deployed in the intermediate nodes. The currently dominant AIMD congestion control, coupled with the RED queue in the core network, has been acknowledged as one of the key factors to the overwhelming success of the Internet. In this thesis, the AIMD/RED system, based on the fluid-flow model, is systematically studied. In particular, we concentrate on the system modeling, stability analysis and bounds estimates. We first focus on the stability and fairness analysis of the AIMD/RED system with a single bottleneck. Then, we derive the theoretical estimates for the upper and lower bounds of homogeneous and heterogeneous AIMD/RED systems with feedback delays and further discuss the system performance when it is not asymptotically stable. Last, we develop a general model for a class of multiple-bottleneck networks and discuss the stability properties of such a system. Theoretical and simulation results presented in this thesis provide insights for in-depth understanding of AIME/RED system and help predict and control the system performance for the Internet with higher data rate links multiplexed with heterogeneous flows.

The purpose of thesis is to investigate the transient stability and operation feasibility of power islanding with different type of dispersed generation in distribution system. A substation of Taipower system is selected for case study to simulate the system transient stability. The mathematical models of dispersed generations including exciters, governors of gas turbine and pitch controller of wind-driven induction generator are used in the simulation program. To represent the load behavior more accurately, the load ratio of residence, commercial, industrial customer class and the composition of electric equipments in feeder, such as induction motors, air conditioners etc, have been identified through load survey study. The load models of end users are employed in simulation to solve the power consumption as function of bus voltage and system frequency. Besides, the dynamic model of induction motors is integrated to solve more accurate system power demand under transient condition. The simulation analysis of transient stability is executed for unbalance distribution system with dispersed generations of gas turbines and wind-driven turbines with three operations sceneries after the distribution system has been disconnected from Taipower system. Different load shedding schemes and output power control of dispersed generation are considered to maintain the stable operation of islanding power system. It is suggested that the system reliability of power system can be enhanced by the dispersed power generation with proper design of load shedding in the transient stability analysis.

the 18th World Congress The International Federation of Automatic Control, Milano (Italy), August 28 - September 2, 2011

The most common way to analyze slope stability is to employ limit equilibrium (LE) theory and obtain a factor of safety (FOS). Methods of LE analysis balance the forces, and/or moments that are driving and resisting slope movement. Generally, in geotechnical engineering practice, a slope that plays host to an important structure is designed with a minimum factor of safety (FOS) of 1.5 and slope movement is monitored throughout the structure’s serviceable life. No further analysis of slope stability is completed until failure occurs when a back analysis is undertaken for the design of remedial measures. This thesis builds on current methods to demonstrate a framework for analysis that can be followed to analyze the state of a slope throughout its serviceable life. The two bridges at North Battleford, Saskatchewan (Battlefords bridges) were used as case studies for this work. In 1967, the older of the two bridges experienced a slope failure at its south abutment immediately prior to its opening to the public. The failure was remediated reactively by means of subsurface drainage, a toe berm, and river training that included diversion/spur dikes to reduce scour at the landslide toe. Since remediation, there has been no other catastrophic failure at either bridge but slow movement continues in the south abutment slope. Laboratory data and field observations from the onsite inclinometers were provided by Clifton Associates Ltd. (CAL) and Saskatchewan Ministry of Highways and Infrastructure (SMHI). The following methodology was followed to develop a framework of analysis for low FOS slopes: 1. Synthesis of data collected during previous investigations at the Battlefords bridges; 2. Detailed site characterization using existing research and terrain analysis; 3. Back analysis of the critical section through original failure using traditional limit equilibrium methods to calibrate the soil strength properties; 4. Application of the calibrated soil strength properties to the original failure after remediation; 5. Estimation of unknown soil properties using instrumentation at the site. 6. Create a model of the new bridge south abutment with the calibrated strength properties from steps 4 & 5 using the finite element method (FEM). 7. Confirmation of the mechanism of failure and assessment of the shear strain and mobilized shear strength; and, 8. Comparison of the results of FEM and LEM models and relationship between factor of safety and mobilized shear strength. The framework presented in this thesis presents a method of modeling the instability of a slope. In the absence of triaxial testing data, it presents a range of mobilized shear strengths along the shear plane.

On August 15, 2007, Pisco, Peru was hit by an earthquake of Magnitude (Mw) = 8.0 which triggered multiple liquefaction induced lateral spreads. The subduction earthquake lasted for approximately 100 seconds and showed a complex rupture. From the geotechnical perspective, the Pisco earthquake was significant for the amount of soil liquefaction observed. A massive liquefaction induced seaward displacement of a marine terrace was observed in the Canchamana complex. Later analysis using the pre- and post-earthquake images showed that the lateral displacements were concentrated only on some regions. Despite the lateral homogeneity of the marine terrace, some cross-sections showed large displacements while others had minimal displacements. The detailed documentation of this case-history makes it an ideal case-study for the determination of the undrained strength of the liquefied soils; hence, the main objective of this research is to use the extensive data from the Canchamana Slide to estimate the shear strength of the liquefied soils. In engineering practice, the undrained strength of liquefied soil is typically estimated by correlating SPT-N values to: 1) absolute value of residual strength, or 2) residual strength ratio. Our research aims to contribute an important data point that will add to the current understanding of the residual strength of liquefied soils. / Master of Science

In this dissertation, we investigate the Riccati diagonal stability and explore some extensions of this notion. Riccati diagonal stability plays an important role in the stability analysis of linear time-delay systems. It is known that if a linear time-delay system is Riccati diagonally stable then it admits a diagonal Lyapunov-Krasovskii functional. The existence of such a functional implies the asymptotic stability of the linear time-delay system. This diagonal stability problem has other applications in applied areas such as physical sciences and population dynamics. We also study the Lyapunov diagonal stability, which has a clear connection to the Riccati diagonal stability. Using a separation theorem, we first provide new proofs for some existing results on the Lyapunov-type diagonal stability. We also construct a new, shorter, and more transparent proof for a well-known result by Kraaijevanger that gives explicit conditions for the Lyapunov diagonal stability on matrices in $\mathbb{R}^{3 \times 3}$. In addition, we give several necessary and sufficient conditions for matrices in $\mathbb{R}^{3 \times 3}$ to be Lyapunov diagonally stable. Furthermore, we present an extension of the so-called Riccati diagonal stability to the Riccati $\alpha$-scalar stability. We derive two new characterizations regarding the Riccati $\alpha$-scalar solution of the Riccati matrix inequality so as to expand and broaden the relevant existing results. We also generalize this notion to consider a common $\alpha$-scalar solution for a family of Riccati matrix inequalities. We shall refer to this new generalization as common Riccati $\alpha$-scalar stability. As an application for the main results, we further explore families of block triangular matrices. Finally, motivated by recent developments, we formulate the problem of Riccati $\alpha$-stability. We present a necessary and sufficient condition for this type of stability and study the connection between Riccati $\alpha$-stability of a pair of $\alpha$-block matrices and Riccati stability of the diagonal block pairs. Moreover, we generalize the Riccati $\alpha$-stability by considering a family of pairs of $\alpha$-block matrices and give a new characterization for this new case.

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This works focuses on analyzing ac/dc hybrid power systems with large number of power converters that can be used for a variety of applications. A computer model of a sample power system is developed. The system consists of various detailed/switching models that are connected together to study the sample system dynamic behavior and to set conditions for safe operation. The stability analysis of this type of power systems has been approached using time domain simulations. There are three types of stability analysis that are studied: steady-state, small-signal analysis and large signal analysis. The steady-state stability analysis is done by investigating the nominal operation of the power electronics system proposed. The small-signal stability of this system is studied by running different parametric case studies. First, the safe values of the main system parameters are defined from the view of the stability of the complete system. Then, these different critical parameters of the system are mapped together to predict their influence on the system. The large signal stability is examined through the response of the power system to different types of transient changes. There are different load steps applied to the critical parameters of the system at the maximum or minimum stability boundary limit found by the mapping section. The maximum load step after which the system can recover and remain stable is defined. The other type of large signal stability analysis done is the study of faults. There are different faults to be studied; for example, over voltage, under voltage and over current. / Master of Science

Shallow flows are those whose width is significantly larger than their depth. In these types of flows, two dimensional coherent structures can be generated and can influence the flow greatly by the lateral transfer of mass and momentum. The development of coherent structures as a result of flow instabilities has been a topic of interest for environmental fluid mechanics for decades. Studies on the use of linear modal stability analysis is commonly found in literature. However, the relatively recent development in the field of hydrodynamic stability suggests that the traditional linear modal stability analysis does not describe the behaviour of the perturbations in finite time. The discrepancy between asymptotic behaviour and finite time behaviour is particularly large in shear driven flows and it is most likely to be the case for shallow flows. This study aims to provide a better understanding of finite time growth of perturbation energy in shallow flows. The three cases of shallow flows evaluated are the mixing layer, jet and wake. The critical cases are obtained through the linear modal analysis and nonmodal analysis was conducted to show the transient behaviour in finite time for what is so-called marginally stable. Finally, the thesis concludes by generalizing the finite time energy growth in the S-k space.