Difference equations of the form X(t) = F*(t)X(t - 1)F(t) - F*(t)X(t - 1)G(t)[I + G*(t)X(t - 1)G(t)]-1G*(t)X(t - 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = (Q(F)F*-GG*)(t) are studied. Solution Of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.
A Comparison Theorem For Matrix Riccati Difference-equations
PAVON, MICHELE
1992
Abstract
Difference equations of the form X(t) = F*(t)X(t - 1)F(t) - F*(t)X(t - 1)G(t)[I + G*(t)X(t - 1)G(t)]-1G*(t)X(t - 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = (Q(F)F*-GG*)(t) are studied. Solution Of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.
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