so swiftly that it feels like yesterday when I first walked the corridors of the Delft Center for Systems and Control (DCSC). At the same time, I cherish all the countless memories that bound my heart to this place and to the people whom I worked with and walked those corridors with day by day. I owe many people a lot for their support, encouragement, and advice, which have contributed directly or indirectly to this thesis and the scientific research associated with it.Besides these general words of gratitude, a number of people deserves special attention. First, I would like to express my thanks towards my supervisors Paul Van den Hof and Peter Heuberger for their excellent guidance and friendship over the years. They were always there helping to find the missing wheel or rejoicing in the success of a breakthrough. Their support both in terms of research and personal matters made my life a lot easier. I also would like to thank Carsten Scherer for many discussions. His ability to understand abstract ideas sharply from half words or bad notation always amazes me.However, my greatest thanks go to my wife Andrea, whose tender love has been a miracle in my life. She was always there in these years, in every moment, supporting me to accomplish all that I was aiming at. She is more than I could ever wish for, as she is all that I would ever need. Last but not least, I thank our son Sándor for all the drawings and stamps he made on my manuscripts to make his father happy and also our daughter Lujza for the smiles to warm my heart. They always worked. It is to them whom I dedicate this thesis.

a b s t r a c tThe identification of linear parameter-varying systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive colored noise. In the Box-Jenkins and output-error cases, it is shown that the currently available linear regression and instrumental variable methods from the literature are far from being optimal in terms of bias and variance of the estimates. To overcome the underlying problems, a refined instrumental variable method is introduced. The proposed approach is compared to the existing methods via a representative simulation example.

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a b s t r a c tModel-based control strategies are widely used for optimal operation of chemical processes to respond to the increasing performance demands in the chemical industry. Yet, obtaining accurate models to describe the inherently nonlinear, time-varying dynamics of chemical processes remains a challenge in most model-based control applications. This paper reviews data-driven, Linear Parameter-Varying (LPV) modeling approaches for process systems by exploring and comparing various identification methods on a high-purity distillation column case study. Several LPV identification methods that utilize input-output and series expansion model structures are explored. Two LPV identification perspectives are adopted: (i) the local approach, which corresponds to the interpolation of Linear Time-Invariant (LTI) models identified at different steady-state operating points of the system and (ii) the global approach, where a parametrized LPV model structure is identified directly using a global data set with varying operating points. For the local approach, various model interpolation schemes are studied under an Output Error (OE) noise setting, whereas in the global case, a polynomial parametrization based OE prediction error minimization approach, an Orthonormal Basis Functions (OBFs) based model estimator and a LeastSquare Support Vector Machine (LS-SVM) based non-parametric approach are investigated. Through extensive simulation studies, the aforementioned LPV identification approaches are analyzed in terms of the attainable model accuracy and local frequency response behavior of the obtained models. Recommendations are provided to achieve adequate choice between the methods for a particular process system at hand.

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Abstract-In this paper we present a Kalman-style realization theory for linear parameter-varying state-space representations whose matrices depend on the scheduling variables in an affine way (abbreviated as LPV-SSA representations). We show that such a LPV-SSA representation is a minimal (in the sense of having the least number of state-variables) representation of its input-output function, if and only if it is observable and span-reachable. We show that any two minimal LPV-SSA representations of the same input-output function are related by a linear isomorphism, and the isomorphism does not depend on the scheduling variable. We show that an input-output function can be represented by a LPV-SSA representation if and only if the Hankel-matrix of the input-output function has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart of partial realization theory for LPV-SSA representation and prove correctness of the KalmanHo algorithm formulated in [1]. These results thus represent the basis of systems theory for LPV-SSA representation.