Stability-preserving model reduction for linear and nonlinear systems arising in analog circuit applications

[摘要] (cont.) These constraints can be used to formulate a semidefinite optimization problem whose solution is an optimal stabilizing projection framework. The second technique is a projection-based model reduction approach for highly nonlinear systems that is based on the trajectory piecewise linear (TPWL) method. Enforcing stability in nonlinear reduced models is an extremely difficult task that is typically ignored in most existing techniques. Our approach utilizes a new nonlinear projection in order to ensure stability in each of the local models used to describe the nonlinear reduced model. The TPWL approach is also extended to handle parameterized models, and a sensitivity-based training system is presented that allows us to efficiently select inputs and parameter values for training. Lastly, we present a system identification approach to model reduction for both linear and nonlinear systems. This approach utilizes given time-domain data, such as input/output samples generated from transient simulation, in order to identify a compact stable model that best fits the given data. Our procedure is based on minimization of a quantity referred to as the ;;robust equation error;;, which, provided the model is incrementally stable, serves as up upper bound for a measure of the accuracy of the identified model termed ;;linearized output error;;. Minimization of this bound, subject to an incremental stability constraint, can be cast as a semidefinite optimization problem.

[发布机构] Massachusetts Institute of Technology