Physical processes which are governed by differential equations or difference equations with discontinuous behavior can be modeled as jump systems. An important type of jump systems is the one evolving linearly among the discrete events; this type of systems is called jump linear systems. A common analysis approach is to employ stochastic processes to describe the sequences, switches, and statistic properties of the discrete events. In this thesis, the jump linear systems to be studied are governed by semi-Markov processes. This type of jump linear systems is called the semi-Markov jump linear system. Due to the nature of the jump linear system, it finds many applications in networked control systems, fault tolerant control systems, and other systems subject to abrupt changes. It is worthwhile to mention that the well studied Markov jump linear system is a special case of the semi-Markov jump linear system. The thesis consists of two parts: The analysis and synthesis of semi-Markov jump linear systems and networked dynamic systems. In Chapter 2 and Chapter 3, the stochastic stability and optimal control for semi-Markov jump linear systems with or without time delays are investigated. In Chapter 4, a novel fault tolerant control scheme is proposed based on the semi-Markov jump linear system stability conditions. Chapter 5 to Chapter 7 discuss the networked dynamic systems analysis via jump linear system approaches. The stochastic stability conditions for semi-Markov jump linear systems are firstly derived. The Lyapunov theory is used to establish the sufficient stability conditions by deriving the infinitesimal generator of the Lyapunov function. Since in practice, almost all the system models could not be identified precisely, robust control problems for systems with uncertainties are investigated based on the established stability conditions. Considering the potential applications on networked systems where time delays are inevitable, optimal control problems for systems with time-varying delays have been studied. In the fault tolerant control design, the semi-Markov process is ideal to characterize time-varying failure rates of the system components whose life time is not exponentially distributed. The designed controller is capable of maintaining the stability when an actuator malfunctions. In the networked control system analysis, stochastic processes are used to model time delays and sensor scheduling rules. Network limitations are compensated by considering more historical information or planning for all possible delays that happen in the future. Both simulations and experiments show the improvements of the control performance by using the proposed techniques. A networked haptic system is investigated via the switching system approach. In the haptic system, the avatar interacts one-dimensionally with a multi-material virtual wall in the virtual environment.The random trajectory along which the avatar moves upon the wall is modeled by stochastic processes, then the multi-material virtual wall rendering is achieved. Finally, the thesis work is summarized and two future research topics are proposed. One is on the networked control system design where delays are modeled by semi-Markov processes, and the other one is on the event-trigger scheme design for networked dynamic systems. / Graduate / 0548 / 0544 / 0546 / jihuang@uvic.ca

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The development of a DC-DC converter for use in a proposed range of one to ten kilowatt off-line power supplies is presented. The converter makes good use of established design practices and recent technical advances. The thesis begins with a review of traditional design practices, which are used in the design of a 3kW, 48V output DC-DC converter, as a bench-mark for evaluation of recent technical advances. Advances evaluated include new converter circuits, control techniques, components, and magnetic component designs. Converter circuits using zero voltage switching (ZVS) transitions offer significant advantages for this application. Of the published converters which have ZVS transitions the phase shift controlled full bridge converter is the most suitable, and assessments of variations on this circuit are presented. During the course of the research it was realised that the ZVS range of one leg of the phase shift controlled full bridge converter could be extended by altering the switching pattern, and this new switching pattern is proposed. A detailed analysis of phase shift controlled full bridge converter operation uncovers a number of operational findings which give a better and more complete understanding of converter operation than hitherto published. Converter design equations and guidelines are presented and the effects of the new improvement are investigated by an approximate analysis. Computer simulations using PSPICE2 are carried out to predict converter performance. A prototype converter design, construction details and test results are given. The results obtained compare well to the predicted performance and confirm the advantages of the new switching pattern.

In the last twenty years, industrial and academic research has produced over one hundred new converter topologies for drives applications. Regrettably, most of the published work has been directed towards a single topology, giving an overall impression of a large number of unconnected, competing techniques. To provide insight into this wide ranging subject area, an overview of converter topologies is presented. Each topology is classified according to its mode of operation and a family tree is derived encompassing all converter types. Selected converters in each class are analysed, simulated and key operational characteristics identified. Issues associated with the practical implementation of analysed topologies are discussed in detail. Of all AC-AC conversion techniques, it is concluded that softswitching converter topologies offer the most attractive alternative to the standard hard switched converter in the power range up to 100kW because of their high performance to cost ratio. Of the softswitching converters, resonant dc-link topologies are shown to produce the poorest output performance although they offer the cheapest solution. Auxiliary pole commutated inverters, on the other hand, can achieve levels of performance approaching those of the hard switched topology while retaining the benefits of softswitching. It is concluded that the auxiliary commutated resonant pole inverter (ACPI) topology offers the greatest potential for exploitation in spite of its relatively high capital cost. Experimental results are presented for a 20kW hard switched inverter and an equivalent 20kW ACPI. In each case the converter controller is implanted using a digital signal processor. For the ACPI, a new control scheme, which eliminates the need for switch current and voltage sensors, is implemented. Results show that the ACPI produces lower overall losses when compared to its hardswitching counterpart. In addition, device voltage stress, output dv/dt and levels of high frequency output harmonics are all reduced. Finally, it is concluded that modularisation of the active devices, optimisation of semiconductor design and a reduction in the number of additional sensors through the use of novel control methods, such as those presented, will all play a part in the realisation of an economically viable system.

Conventional 'hard switching' converters suffer from significant switching loss due to the simultaneous imposition of high values of current and voltage on the devices during commutation. Resonant converters offer a solution to this problem. A review of resonant circuit topologies is presented, which includes a summary of the interference problems which may occur when using power converters in the rail traction environment. Particular attention is given to the Resonant DC Link Inverter (RDCLI) which shows a great deal of pronuse using currently available devices. The frequency domain simulation of RDCLIs is discussed as a means of rapidly evaluating circuit behaviour, especially in relation to modulation strategies. A novel modulation strategy is proposed for Resonant DC Link Inverters, based on a procedure known as Simulated Annealing which allows complex harmonic manipulations such as han-nonic minimisation, to be performed. This is despite the fact that RDCLIs are constrained to use Discrete Pulse Modulation whereby switch commutations are restricted to specific moments in time. The modulation algorithms were verified by use of a low-power test rig and the results obtained are compared against theoretical values. Details of the hardware implementation are also included. A single-phase pulse-converter input stage is described which may be incorporated into the Resonant DC Link Inverter topology. This input stage also benefits from soft-sVVItching and allows four-quadrant operation at any desired power factor. A modulation scheme based on SiMulated Annealing is proposed for the pulse-converter, to achieve hannomc control whilst also synchronising with the supply wavefon-n. Practical results are presented and compared with those obtained by simulation and calculation. Finally the design of Resonant DC Link Converters is discussed and reconunendations made for the choice of resonant components based on the minimisation of overall losses. Comparisons are made between hard-switching and soft-switching converters in terms of loss and harmonic performance, in an attempt to quantify the benefits which may be obtained by the application of soft-switching.

This thesis has to do with certain fundamental queues that are well established as models for delay in simple packet-switching concentrators and networks. We first revisit the single server queue with Poisson arrivals and general independent service times. We then work out a complete delay analysis for a traffic concentrating tandem network of queues with deterministic service and batch Poisson sources connected to every node; this is the most comprehensive analysis available for a network which is not of Jackson type. We also show how to (partially) extend the analysis to a concentrating tree network, and to an arrival process somewhat more general that batch Poisson. / The two parts of the thesis have a close methodological relationship. Our contribution in both cases is to rederive certain known results, and to produce a variety of new ones, using techniques that are essentially qualitative. Our particular view of the stochastic processes in question is guided by a very special queue discipline, namely Last Come First Served preemptive resume; by identifying certain structural features of the sample paths, one can read, almost without calculation, a host of statistics of common interest. The LCFS preemptive resume discipline also enables us: (i) to strengthen the connection between the single server queue with general independent service times and interarrival times, and the fluctuation theory of random walks; (ii) to strengthen the connection between the queue with Poisson arrivals and branching processes.

This study examined structural constraints on early child code mixing. Constraints are widely attested in adult bilinguals (Myers-Scotton, 1993; Poplack, 1980). It has been argued that these constraints preserve the structural properties of both languages. It is uncertain whether constraints on early child code mixing are the same as constraints on adult code mixing. The present analysis was based on Poplack's two structural constraints: the free morpheme and the equivalence constraints. Ten French-English bilingual subjects were observed at 4 time periods, between approximately 2;00 and 3;06 years of age. The children's utterances containing elements from both languages were analysed for violations of Poplack's constraints. The violation rate was extremely low, less than 2% of the total mixed utterances. These results corroborate Lanza (1997), Vihman (1998), Allen et al. (2000), and Paradis et al. (2000), who likewise found that structural constraints on code mixing are operational from early in acquisition.

Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples. We develop a number of techniques for pricing American options by solving the system of partial differential equations in a general \mathcal{K}-state regime-switching model. The linear complementarity problem is replaced by either the penalty or the direct control formulations. With an implicit discretization, we compare a number of iterative procedures (full policy iteration, fixed point-policy iteration, and local American iteration) for the associated nonlinear algebraic equations. Specifically, a linear system appears in the full policy iteration which can be solved directly or iteratively. Numerical tests indicate that the fixed point-policy iteration and the full-policy iteration (using a simple iteration for the linear system), both coupled with a penalty formulation, results in an efficient method. In addition, using a direct solution method to solve the linear system appearing in the full policy iteration is usually computationally very expensive depending on the jump parameters. A Fourier transform is applied to the system of partial differential equations for pricing American options to obtain a linear system of ordinary differential equations that can be solved explicitly at each timestep. We develop the Fourier space timestepping algorithm which incorporates a timestepping scheme in the frequency domain, in which the frequency domain prices are obtained by applying the discrete Fourier transform to the spatial domain. Close to quadratic convergence in time and space is observed for all regimes when using a second order Crank-Nicolson scheme for approximation of the explicit solution of the ordinary differential equation.

The paper provides a model that assesses the set of complementary components of varying compatibility and its effect towards consumer adoption decisions. The smartphone market is a system good which utilizes the device and a set of compatible applications (apps). The amount of switching costs may vary depending upon the consumer’s decision to switch devices or across platforms. Analyzing the Android ecosystem, the process of custom ROMs (and rooting) and the large set of games, news, etc. apps justify the existence of device-specific and platform-specific apps. The model reinforces the findings of a survey conducted by UBS suggesting the retention rate (i.e. level of switch costs) of Apple users is higher than Android users. The retention among Android devices is much lower in comparison as well. The model observes that the product fragmentation and the interdependence of apps lead to the noticeably lower retention rates across Android devices and platforms.

This thesis explores option pricing and hedging in a discrete time regime-switching environment. If the regime risk cannot be hedged away, then we cannot ignore this risk and use the Black-Scholes pricing and hedging framework to generate a unique pricing and hedging measure. We develop a risk neutral pricing measure by applying an Esscher Transform to the real world asset price process, with the focus on the issue of incompleteness of the market. The Esscher transform turns out to be a convenient and effective tool for option pricing under the discrete time regime switching models. We apply the pricing measure to both single variate European options and multivariate options. To better understand the effect of the pricing method, we also compared the results with those generated from two other risk neutral methods: the Black-Scholes model, and the natural equivalent martingale method. We further investigate the difference in hedging associated with different pricing measures. This is of interest when the choice of pricing method is uncertain under regime switching models. We compare four hedging strategies: delta hedging for the three risk neutral pricing methods under study, and mean variance hedging. We also develop a more general tool of tail ordering for hedging analysis in a general incomplete market with the uncertainty of the risk neutral measures. As a result of the analysis, we propose that pricing and hedging using the Esscher transform may be an effective strategy for a market where the regime switching process brings uncertainty.