This thesis focuses on the design and implementation of a three-level Class D audio amplifier by applying recently developed sliding-mode quantized control. The designed controller, which consists of the analog filters and logic circuit, switches an H-bridge Class-D amplifier with a lowpass LC filter and operates it in the sliding mode, in order to achieve desired stability and high fidelity in the audio band. The experimental result shows that the lowest THD+N (total harmonic distortion plus noise) can be as low as 0.02% at 1 kHz. The performance is better than most of the available commercial products.

A quantized control means that the control force is restricted to takes only a finite number of prescribed levels. The well-known bang-bang control or relay control belongs to this category. This kind of control has the advantage of simple circuit realization using electronic switches or relays that feature low power consumption in their on-off operation. However, quantized control introduces noise and distortion, and even worse its high nonlinearity makes the stabilizing compensator design difficult. This thesis applies the concept of dynamic sliding mode to the synthesis of a multi-level quantized control, with the aim to stabilize the system, perform reference tracking and attenuate the switching noise. The applicability of the presented sliding-mode quantized control is demonstrated on a three-level buck converter. Compared with the conventional PWM (Pulse-Width Modulation) scheme, it eliminates the use of a complex three-level PWM generator and a current sensor. A 12V/8V three-level buck converter with sliding mode quantized control is designed and realized, which shows the output voltage with 0.4625% of average DC error, 2.8988% of the static output ripple and 2.3% of load regulation error in response to the load current steps from 0A/3A to 3A/0A, at a slew rate of 6.25A/£gsec.

"Dynamics" is very roughly the study of how objects change in time; for instance whether an electrical circuit goes to equilibrium, due to thermal dissipation. By "information", we mean how helpful it is to observe an object in order to know it better, for instance how many binary digits we can acquire on the value of a voltage by an appropriate measure. A "computation" is a physical process, e.g. the flow of current into a complex set of transistors, that after some time eventually gives us the solution of a mathematical problem (such as "Is 13 prime?"). We are interested to various relations between these concepts. In a first chapter, we unify some arguments in the literature to show that a whole class of quantities of dynamical systems are uncomputable. For instance the topological entropy of tilings and Turing machines. Then we propose a precise meaning to the statement "This dynamical system is a computer", at least for symbolic systems, such as cellular automata. We also show, for instance, that a "computer" must be dynamically unstable, and can even be chaotic. In a third chapter, we compare how complicated it is to control a system according whether we can acquire information on it ("feedback") or not ("open loop"). We are specifically interested in finite-state systems. In last chapter we show how to control a scalar linear system when only a finite amount of information can be acquired at every step of time.