Filtering and Control by means of LMI optimisation
Francesco Alessandro Cuzzola - Politecnico di Milano - 
This thesis is divided in two main parts. Part 1 (Chapters 2-6) deals with theoretical LMI concepts whereas in Part 2 (Chapters 7-9) we report some significant applications of LMI-LPV theory. The organisation is as follows. In Chapter 2 we present some significant tools that allow to reduce both classical and non classical control problems into an LMI framework: Shur Lemma, SProcedures, Projection Lemmas, Linear Fractional Transformations, etc. In Chapters 3, 4 and 5 we face the LMI filtering problem for LTI (Linear Time Invariant) systems, LPTV (Linear Periodically Time Varying) system and norm-bounded uncertain systems, respectively. In all these cases we will exploit the unbiasedness condition in order to achieve computationally light LMI synthesis procedures that can be applied to unstable systems as well. In Chapter 6 we present one of the most significant LPV-LMI techniques nowadays available (see [Sch99a]). This technique will be widely exploited in the second part of this thesis. We then turn to the application side. In Chapter 7 we pose the problem of rejecting periodic disturbances in helicopters and we propose to face this problem both by means of a gain scheduling approach of periodic controllers and by means of the LPV design technique described in Chapter 6. Another widely studied problem is represented by the trajectory tracking problem of mobile robots. We have considered this problem having the objective of designing the trajectory tracking control of mobile robot platforms ad the LABMATE platform available care of Laboratorio di Automatica of the Politecnico di Milano. As explained in Chapter 8, this non-linear control problem is faced by switching among LPV technique based on a grid procedure of the parameter space [Apk98]. Finally, in Chapter 9 we propose the use of the LPV technique described in Chapter 6 in order to face a particular type of deconvolution problem i.e. the problem of reconstructing the primary current of non-linear current transformers on the basis of the measurement of the secondary curren...
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