Convergence analysis of special type state observer algorithms of discrete dynamic systems via Lyapunov functions

The parameter values of an observer algorithm that are allowed by the convergence conditions are obtained for a class of nonstationary linear discrete dynamic systems with the only assumption that they are observable. The analysis of the observer convergence conditions reduces to finding the conditions of asymptotic stability of the zero solution of a nonlinear matrix difference equation. This problem is solved with the use of Lyapunov functions. An observer algorithm is proposed for nonlinear discrete systems, and its convergence condition is obtained.