Efficient linearization of explicit multilinear systems using normalized decomposed tensors

Abstract

Multilinear systems allow multiplications of states, inputs, and states with inputs, in all possible combinations. Recently, a new normalized decomposed tensor format of explicit multilinear models was introduced. This paper presents a linearization method for the normalized canonical polyadic decomposed tensor format of explicit multilinear models. The proposed method computes the Jacobian matrix to obtain the linear system evaluated at the equilibrium point. An adaption for large-scale sparse systems is outlined. Performance and computational time are evaluated for different number of states and sparsity structures. The results suggest computational advantages of the explicit multilinear format compared to the non-normalized one. The adaptation to large-scale sparse systems shows clear computational advantage.