Related papers: Model Reduction of Parametric Differential-Algebra…
When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…
We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians…
Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
We consider the problem of constructing reduced models for large scale systems with poles in general domains in the complex plane (as opposed to, e.g., the open left-half plane or the open unit disk). Our goal is to design a model reduction…
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…
We consider linear magneto-quasistatic field equations which arise in simulation of low-frequency electromagnetic devices coupled to electrical circuits. A finite element discretization of such equations on 3D domains leads to a singular…
Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various…
We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and…
Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…
In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on…
This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of…
This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearization techniques. By directly leveraging structural properties…
This work discusses model reduction for differential-algebraic systems with quadratic output equations. Under mild conditions, these systems can be transformed into a Weierstra{\ss} canonical form and, thus, be decoupled into differential…
We consider two approaches to balanced truncation of stochastic linear systems, which follow from different generalizations of the reachability Gramian of deterministic systems. Both preserve mean-square asymptotic stability, but only the…
In this paper, we present an empirical balanced truncation method for nonlinear systems with linear time-invariant input vector field components. First, we define differential reachability and observability Gramians. They are matrix valued…
The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…
A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspace projection model…
We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that…
In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…