Canonical forms for bilinear systems
Systems & Control Letters
Identification and rational L2 approximation: a gradient algorithm
Automatica (Journal of IFAC)
Hankel-type model reduction for linear repetitive processes: differential and discrete cases
Multidimensional Systems and Signal Processing
Technical communique: H∞ model reduction for uncertain switched linear discrete-time systems
Automatica (Journal of IFAC)
Order reduction of bilinear MIMO dynamical systems using new block Krylov subspaces
Computers & Mathematics with Applications
Brief paper: Model reduction of homogeneous-in-the-state bilinear systems with input constraints
Automatica (Journal of IFAC)
Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems
SIAM Journal on Control and Optimization
| Hi-index | 22.15 |
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.