New model reduction scheme for bilinear systems

Model Reduction by Moment Matching for Linear and Nonlinear Systems

“…with ξ(t) ∈ IR ν , is a model at (s(ω), l(ω)) of system (34) if system (41) has the same moment at (s(ω), l(ω)) as (34). In this case, system (41) is said to match the moment of system (34) at (s(ω), l(ω)).…”

“…Suppose Assumptions 1 and 2 hold. The function h(π(ω)), with π(·) solution of equation (37), is the moment of system (34) at (s(ω), l(ω)).…”

“…Energy-based methods have been discussed, for example, in [21], [23], [32], [33]; model reduction of systems in special forms, such as differential-algebraic systems, bilinear systems or mechanical/Hamiltonian systems, have been discussed in [34], [35], [36], [37], [38], and reduction around a limit cycle or a manifold has been discussed in [39], [40]. Some computational issues have been addressed in [41], [42], [40], [27].…”

Model reduction of a class of discrete-time nonlinear systems

“…Further details on available techniques for model reduction are largely discussed in the survey paper [4] and the references therein. Even though model reduction procedures are developed rather properly for linear dynamical systems, there are still many issues in their generalization to the nonlinear case, see e.g., [20][21][22][23][24][25][26]. Among the difficulties that appear in nonlinear model reduction are the absence of general methods that assure global approximation with predefined absolute error, the complexity of the generalization of balancing methods to nonlinear systems, and the problem of stability preserving by projection.…”

Reduction and identification methods for Markovian control systems, with application to thin film deposition

“…If this matrix is a linear function of the inputs, or may be approximated locally as one, then the system of Equations (1) and (2) is classified as a bilinear control system [25]. Tools for identification and reduction of bilinear systems have been generalized from the theory for LTI systems [26][27][28][29]. However, the matrices required for the analysis are much larger than those for LTI systems, making the techniques impractical for systems having more than a few dimensions.…”