Probability of stability calculation of MIMOn cascade non-linear systems with random parameters.

This article addresses the stability analysis of stochastic Multiple n Inputs and Multiple n Outputs (MIMOn) cascade non-linear systems with random parameters, focusing on the probability of stability estimation method. It highlights that MIMOn systems with more than three inputs and outputs (n > 3) can exhibit spatial hyperchaos, a complex chaotic behavior arising from signal propagation through cascades, which may lead to instability. The study develops mathematical criteria for defining the stability region of such systems, applies these to a stochastic MIMO5 (five inputs and five outputs) cascade system with uniformly distributed parameters, and uses bifurcation diagrams, Lyapunov exponents, and spatial phase portraits generated via MATLAB to analyze system dynamics. The findings demonstrate that appropriate selection of parameter intervals can maximize the probability of stability and prevent spatial hyperchaos, offering practical guidance for engineers to enhance the reliability and safety of complex non-linear systems with random parameters.