Spectral properties of metzler dynami̇cal systems

In this thesis, the asymptotic stability of dynamic systems given by Metzler matrices is addressed. Metzler matrices characterize positive linear systems. In the analysis of continuous and discrete-time positive linear systems, the eigenvalue properties of the system matrix come to the fore. Basic results and applications regarding the eigenvalue properties of the Metzler matrices class, which has a wide application area, are given within the scope of this study. Stochastic matrices are a subclass of Metzler matrices. In Markov processes of a dynamic system provided by a stochastic matrix, when an initial state vector of the simplex is given, the probability distribution at any step can be calculated, and the state vector to which the Markov chain converges can also be expressed. Explanatory examples of models that are applications of the Markov chain are given.