Time-limited H2-optimal model order reduction of linear systems with quadratic outputs

An important class of dynamical systems with several practical applications is that of linear systems with quadratic outputs. In time-limited model order reduction, the main goal is to ensure that the reduced-order model preserves the output response of the original system over a specified limited time range. To quantify the error within the specified time interval, this paper derives a mathematical expression for the time-limited H2-norm of linear systems with quadratic outputs, serving as a measure of the reduced model's accuracy over this period. Subsequently, the necessary conditions for achieving a local optimum of the time-limited H2 norm error are derived. The inherent inability to satisfy these optimality conditions within the Petrov-Galerkin projection framework is also discussed. An iterative fixed-point…