Simulation of hybrid MTL systems with random parameters based on stochastic DAEs

The paper deals with a method for the simulation of hybrid systems containing multiconductor transmission lines (MTL) with randomly varying primary parameters. A core of the method lies on a theory of stochastic differential equations (SDE) considering the system responses as stochastic processes. In fact, due to a hybrid nature of the system containing also parts with lumped parameters, a system of stochastic differential-algebraic equations (SDAE) is obtained. The responses are formed by the sets of stochastic trajectories completed by corresponding sample means and confidence intervals. The MTL model is based on a cascade connection of generalized RLCG T-networks and a statevariable method is used to formulate its equations. The boundary conditions are folded in by a modified nodal analysis (MNA) enabling to include the MTLs as parts of arbitrary lumped-parameter circuits. Finally, a backward differentiation formula consistent with the Itô stochastic calculus is used for numerical solutions. All the computer simulations were performed using the Matlab language.