ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

In this paper we consider the existence problem of some global solutions for a general class of discrete-time backward nonlinear equations defined on ordered Banach spaces. The discussed class of nonlinear equations includes as special cases many of the discrete-time Riccati equations arising both in deterministic and stochastic optimal control problems. Based on a linear matrix inequalities (LMI) approach we give necessary and sufficient conditions for the existence of the maximal solution, the stabilizing solution and respectively the minimal positive semi-definite solution of the considered discrete-time backward nonlinear equations. This paper extends the results in [V. Dragan, T. Morozan, A class of discrete time generalized Riccati equations, Journal of Difference Equations and Applications, 1563-5120, 11 December 2009] and [V. M. Ungureanu, Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces, IMA J. Math. Control Inform. 26 (2009), no. 1, 105-127].