A computationally effective time-restricted stability preserving H2-optimal model order reduction approach

Abstract

Several approaches for reducing model order on the definite time segments have become the topic of investigation in a series of papers that bring challenges during application in a large-scale setting. The subject of discussion of this paper is the computationally efficient time-restricted H2-optimal model order reduction method of higher dimensional sparse systems that requires the solutions of time-restricted Lyapunov and Sylvester equations. Our discussion is on developing the algorithms to solve these matrix equations that face difficulty when calculating the matrix exponential of the large-scale matrices. As a result, an efficient remedy is also proposed to compute the matrix exponential. Our ideas are also evaluated for index-1 descriptor systems apart from the generalized structure. Numerical analyses are conducted on several benchmark examples to illustrate how accurate and efficient our suggested approaches are by comparing them with the existing methods.

Keywords

• Time limited model reduction
• H2-optimal condition
• Time-limited Gramians
• Sylvester and Lyapunov equations
• Sparsity
• Matrix exponential