## On $$H_2$$ model reduction of bilinear systems.(English)Zbl 0991.93020

Summary: The $$H_2$$ model reduction problem for continuous-time bilinear systems is studied in this paper. By defining the $$H_2$$ norm of bilinear systems in terms of the state-space matrices, the $$H_2$$ model reduction error is computed via the reachability or observability gramian. Necessary conditions for the reduced order bilinear models to be $$H_2$$ optimal are given. The gradient flow approach is used to obtain the solution of the $$H_2$$ model reduction problem. The formulation allows certain properties of the original models to be preserved in the reduced order models. The model reduction procedure developed can also be applied to finite-dimensional linear time-invariant systems. A numerical example is employed to illustrate the effectiveness of the proposed method.

### MSC:

 93B11 System structure simplification 93C10 Nonlinear systems in control theory 93A30 Mathematical modelling of systems (MSC2010)