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The system dynamics of the systems performing in discrete time can be described using extremal algebras. Extremal algebras help us to solve nonlinear problems and give us the solution to problems that are unsolvable in classical, linear algebra. In dependence on the purpose of the study, various triangular fuzzy t-norms can be used. System can be then described by the transition matrix and the state vectors. In the paper the extremal algebras are introduced together with their practical applications. Also max-t fuzzy algebras (as a subset of extremal algebras) are mentioned, four main triangular norms are described and the solution to the eigenproblem is outlined.