Stochastic dynamics of time correlation in complex systems with discrete time

Stochastic dynamics of time correlation in complex systems with discrete time

In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy S(i)(t) where i=0,1,2,3,ellipsis, as an infor...

Optimal Finite-time Control of Positive Linear Discrete-time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...

Correlation bounds for discrete-time systems with banded dynamics

We consider the steady-state error covariance for a discrete-time system with banded dynamics. Such systems frequently arise from the spatial and temporal discretization of partial differential equations. In such systems, the magnitudes of the entries of the steady-state covariance matrix typically decrease as the distance from the diagonal increases. We obtain a bound on the entries of the cov...

Eigenvalue Assignment Of Discrete-Time Linear Systems With State And Input Time-Delays

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...

Dynamics of a discrete-time plant-herbivore model