Closed Form Solutions for Matrix Linear Systems Using Double Matrix Exponential Functions

The paper presents closed form solutions for a class of matrix linear systems whose state variable is a matrix. The formulation evaluates the state response of the system in terms of the original system matrices. The proposed solutions naturally fit systems which are most conveniently described by matrix processes. Its formulation uses a compact notation referred as double matrix exponential functions, which is an extension of matrix exponential function, for aiding both intuition and mathematical manipulation. It is a straightforward extension of the solutions for ordinary vector linear systems studied in the past several decades and will play an important role in the design of matrix linear systems using original system matrices.