Application of Stochastic Differential-Algebraic Equations in Hybrid MTL Systems Analysis

Abstract

The paper deals with the application of stochastic differential-algebraic equations (SDAE) in the field of the time-domain simulation of hybrid (lumped/distributed) systems with randomly varying parameters. A core of the method lies on the theory of stochastic differential equations (SDE) considering the system responses as stochastic processes. However, due to a hybrid nature of the system, namely its lumped parameter part, non-differential (algebraic) parts arise generally in the solution. Herein, multiconductor transmission lines (MTL) play a role of the distributed-parameter parts of the hybrid system. The MTL model is designed as a cascade connection of generalized RLCG T-networks, while the state-variable method is applied for its description. The MTL boundary conditions are incorporated through a modified nodal analysis (MNA) to cover arbitrarily complex circuits. System responses are formed by the sets of stochastic trajectories completed by corresponding sample means and respective confidence intervals. To get the results a weak stochastic backward Euler scheme is used, consistent with the Itô stochastic calculus. All the computer simulations have been performed in the Matlab language environment.The paper deals with the application of stochastic differential-algebraic equations (SDAE) in the field of the time-domain simulation of hybrid (lumped/distributed) systems with randomly varying parameters. A core of the method lies on the theory of stochastic differential equations (SDE) considering the system responses as stochastic processes. However, due to a hybrid nature of the system, namely its lumped parameter part, non-differential (algebraic) parts arise generally in the solution. Herein, multiconductor transmission lines (MTL) play a role of the distributed-parameter parts of the hybrid system. The MTL model is designed as a cascade connection of generalized RLCG T-networks, while the state-variable method is applied for its description. The MTL boundary conditions are incorporated through a modified nodal analysis (MNA) to cover arbitrarily complex circuits. System responses are formed by the sets of stochastic trajectories completed by corresponding sample means and respective confidence intervals. To get the results a weak stochastic backward Euler scheme is used, consistent with the Itô stochastic calculus. All the computer simulations have been performed in the Matlab language environment.