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The contributions of this thesis address both researchers and practicing engineers working in the field of process monitoring and control. Operators and manufacturers of plants arising in the chemical or thermal process industry are exposed to global competition and an increasing demand for product quality and optimality in plant operation (e.g. regarding to energy consumption) not only advocates but rather enforces the use of detailed, physical models in plant monitoring, automatic control and optimization. A large number of plants arise in the form of transport process systems, which are formally described by (quasi-) linear systems of first order partial differential equations (PDEs). For the formal description of the plant to be a valuable tool in control and optimization, the parameters must be adjusted, s.t. the input/output-behaviour of the model and the process match. The data is usually given in form of a sequence of measurements, i.e. sampled data. Consequently, we devise an estimator, that (i) explicitly accounts for the distributed parameter characteristic of the plant, i.e. it does not rely on finite dimensional approximations of the system of PDEs, and (ii) accounts for the fact, that only sampled data is available for estimation. By employing the geometrical interpretation of a system of first order PDEs with a single characteristic speed and direction and an appropriate choice of window of data used in the procedure, we keep the computational effort of finding a suitable set of process parameters as small as possible. The second contribution of this thesis can be summarized in a careful study of observability properties of transport process systems using sampled data. We review some fundamentals of semigroup theory, which put us in a position to study the evolution of the infinite dimensional plant from one sampling instant to the next. The conclusions we can draw from these considerations provide a practical basis for finite dimensional, optimal controller and observer design in discrete time and facilitate the formally seamless integration of the plant in the digital process control framework. Experimental results obtained from a pilot plant in the thermal process industry point out the usefulness of the two major contributions of this thesis in industrial practice.