An approach to analysis and design for some large-scale linear systems

Abstract

For a linear time invariant system, the system stability is equivalent to the stability of the system matrix. Thus, finding the conditions for the matrix stability becomes a key to analysis and design of large-scale linear systems. This paper is aimed at studying the large-scale matrix stability problem by means of matrix partitioning. The sufficient conditions for the large-scale matrix stability are proposed. For matrices with normal block diagonal submatrices, a concise and practical expression for testing matrix stability is derived. Additionally, for block diagonally dominant matrices, a sufficient condition, which is used to determine whether the matrix is stable, is proposed. Finally, numerical examples are provided that not only validate theoretical results obtained in this paper, but also demonstrate the analysis and design of large-scale linear systems.