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Superposition laws for solutions of differential matrix Riccati equations arising in control theory

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2 Author(s)
M. Sorine ; Institut National de Recherche en Informatique et an Automatique, Le Chesnay, France ; P. Winternitz

Representation formulas are given for the general solution of the N \times N matrix Riccati equation \dot{W} = A + WB + CW + WDW using n known solutions, with n = 1, ..., 5 ( n -representations). The 5- representation is a superposition formula, in that it expresses the general solution explicitly as a function of five particular solutions and N2arbitrary constants ( N \geq 2 ), using no further information. The representation formulas can be used in numerical calculations. The 4- and 5- representations are specially useful when a solution W(t) has a singularity for some finite t = t_{0} . They also clarify the properties of the solution space: the matrix elements of W(t) are meromorphic functions of t having simple poles as the only possible singularities. The relation between the representation formulas and previously known results is discussed.

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IEEE Transactions on Automatic Control  (Volume:30 ,  Issue: 3 )