Model reduction of discrete-time bilinear systems by a Laguerre expansion technique

• Laguerre-based reduction for discrete-time bilinear systems is proposed.
• Laguerre coefficients can be obtained recursively and have a nice structure.
• The potential singularity is avoided by using an enlarged subspace.
• The terminal reduction is introduced to provide a modified algorithm.

In this paper, we investigate model reduction of discrete-time bilinear control systems using a Laguerre expansion technique. The transfer function of systems is expanded under the Laguerre functions basis and we show that Laguerre coefficients take on a recursion relationship, which allows us to execute the reduction elegantly based on the recursion, instead of the cumbersome expression of Laguerre coefficients. Then reduced models are produced in the framework of two-sided projection methods and a certain number of Laguerre coefficients of the original systems are preserved implicitly, thereby resulting in a good approximation. Noting that the order of reduced models may rise rapidly, a terminal reduction method is introduced to modify our algorithm. The modified algorithm is achieved by properly defining an auxiliary system, significantly shrinking the order of reduced models. Theoretical analysis and numerical experiments show the efficiency of our approach.