Related papers: Interpolatory Necessary Optimality Conditions for …
Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling of…
We develop a unifying framework for interpolatory $\mathcal{L}_2$-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally…
In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality…
In this paper we establish the interpolatory model reduction framework for optimal approximation of MIMO dynamical systems with respect to the $\mathcal{H}_2$ norm over a finite-time horizon, denoted as the $\mathcal{H}_2(t_f)$ norm. Using…
Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence,…
This paper presents an interpolatory framework for time-limited $H_2$ optimal model order reduction named Limited Time Iterative Rational Krylov Algorithm (LT-IRKA). The algorithm yields high fidelity reduced order models over limited time…
Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear…
In this paper we compute families of reduced order models that match a prescribed set of moments of a highly dimensional linear time-invariant system. First, we fully parametrize the models in the interpolation points and in the free…
This paper addresses the $\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive…
We develop the interpolatory $\mathcal{H}_2$ optimal model reduction framework for linear control systems posed on infinite dimensional state, input and output spaces. Specifically, we consider linear systems formulated as controlled…
In this paper, the problems of frequency-limited and time-limited H2-optimal model order reduction of linear time-invariant systems are considered within the oblique projection framework. It is shown that it is inherently not possible to…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
In this paper, we investigate the optimal $\mathcal{H}_2$ model reduction problem for single-input single-output (SISO) continuous-time linear time-invariant (LTI) systems. A semi-definite relaxation (SDR) approach is proposed to determine…
In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods…
In this paper, the $\mathcal{H}_{2}$ optimal approximation of a $n_{y}\times{n_{u}}$ transfer function $\mathbf{G}(s)$ by a finite dimensional system $\hat{\mathbf{H}}_{d}(s)$ including input/output delays, is addressed. The underlying…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an…
This paper develops an interpolatory framework for weighted-$\mathcal{H}_2$ model reduction of MIMO dynamical systems. A new representation of the weighted-$\mathcal{H}_2$ inner products in MIMO settings is introduced and used to derive…
We address the problem of learning the parameters of a stable linear time invariant (LTI) system or linear dynamical system (LDS) with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus…
In this contribution, a new framework for H2-optimal reduction of multiple-input, multiple- output linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential…