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Explicit Solution for a Class of Discrete‐Time Algebraic R iccati Equations
Author(s) -
Rojas A. J.
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.511
Subject(s) - riccati equation , mathematics , eigenvalues and eigenvectors , algebraic number , class (philosophy) , algebraic riccati equation , linear quadratic regulator , dual (grammatical number) , discrete time and continuous time , quadratic equation , state (computer science) , quadratic growth , mathematical optimization , mathematical analysis , optimal control , differential equation , computer science , algorithm , art , statistics , physics , geometry , literature , quantum mechanics , artificial intelligence
In the present paper we obtain an explicit closed‐form solution for the discrete‐time algebraic R iccati equation ( DTARE ) with vanishing state weight, whenever the unstable eigenvalues are distinct. We discuss links to current algorithmic solutions and observe that the AREs in such a class solve on one hand the infimal signal‐to‐noise ratio ( SNR ) problem, whilst on the other hand, in their dual form they solve a K alman filter problem. We then extend the main result to an example case of the optimal linear quadratic regulator gain. We relax some of the assumptions behind the main result and conclude with possible future directions for the present work.