One way for the probability of stability estimation of discrete systems with randomly chosen parameters

Analysis and control of spatial limit sets and spatial chaos appearance in mimo cascade connected nonlinear systems

“…The above shows that there is an analogy between mathematical models of nonlinear discrete systems (14) and (15) and MIMO cascade connected nonlinear system (13). Also, the use of the same necessary conditions for limit sets existence and sufficient condition for limit sets absence is validated.…”

“…It can be concluded by comparing models (13) and (15), that each cascade represents one iteration of nonlinear discrete system (15). In Fig.…”

“…In Fig. 3 there are k + 1 cascades, and in the state space model (15) there are k + 1 iterations in total. In the case of cascade system (13), iteration is not running through time as is the case of system (15), but rather in space.…”

“…. State coordinates of nonlinear discrete system (15) calculated for the ith iteration, in the case of nonlinear cascade system (13), represent the output vector of the ith cascade, i = 1, …, k + 1..…”

The Probability of Stability Estimation of an Arbitrary Order DPCM Prediction Filter: Comparison between the Classical Approach and the Monte Carlo Method

“…We can easily achieve satisfied accuracy, but we perform more experiments again for the second-order predictor, because we also know the exact value of the probability of stability, and furthermore, for higher-order predictors we adopt a number of trials large enough for our purpose. In order to compare accuracy of different methods, we will show how the errors occur if we use some alternative approximate methods [6,7,27].…”