Titlebook: Reduced Order Systems; Ali A. Jalali,Craig S. Sims†,Parviz Famouri Book 2006 Springer-Verlag Berlin Heidelberg 2006 Reduced Order Filterin

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0170-8643 d, and state space system representation is used throughout the book. It provides a coherent view of the recent theory of reduced order theory and its applications including a wide range of application problems, solutions and unresolved issues..978-3-540-34358-5978-3-540-34359-2Series ISSN 0170-8643 Series E-ISSN 1610-7411

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6 Stochastic Control over Finite Time Intervals,paration theorem [4], is probably the most elegant result in all of systems theory. We will begin our examination of Stochastic Control problems by examining the output feedback control problem which has been studied by Axsater [5].

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1 Introduction,examples of this aspect of control engineering have become widely known. For example Wiener filtering [1], has provided us a method of optimizing the design of constant coefficient linear filter to reduce the impact of noise. This work was thought to be so useful that it was classified during World

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2 Static Problems,em order inherently has to do with how the state of a system evolves in time, i.e. with the order of the differential or difference equations considered. Some insight into how one proceeds, however, can be gained by looking at the static case, and one can get some idea of the difficulties involved.

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3 Stationary Processes,on involving only algebraic equations rather than differential equations. This setting is in terms of time invariant linear systems driven by white noise processes. The basic assumption is that the processes considered are in steady state in a statistical sense, with a bounded constant second moment

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5 Smoothing, the interval. Such problems have the characteristics that they have non causal solutions and so may not be implemented in real time. Since this is the case, the reader may wonder why we would be interested in a reduced order sub optimal solution, as obtained in [1] instead of a full order optimal s

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6 Stochastic Control over Finite Time Intervals,t all, is of secondary importance. We shall discuss problems with and without dynamic compensators. Dynamic compensators are important for the case when full state measurements are not available, so that an observer is useful [1]. They are also important for the case where only a noisy measurement o

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7 Innovation Approach to Reduced Order Estimation,process.” The concept of “reduced order innovation process” we feel captures the qualitative essence of how useful information is extracted from the given measurements when a reduced order estimator is used.

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8 Linear Two-Point Boundary Value Processes,is interest reflects a desire to estimate processes governed by ordinary differential equations with constraints at each end point of an interval. TPBVP’s occur frequently in physics and engineering. For example, partial differential equations in temporal steady-state often lead to TPBVP’s.