In this short note, a non-intrusive data-driven formulation of ADI-based low-rank balanced truncation is provided. The proposed algorithm only requires transfer function samples at the mirror images ADI shifts. If some shifts are used in both approximating controllability Gramian and observability Gramian, then function's derivative these also needed to enforce Hermite interpolation Loewner framework. It noted that can be viewed as two-step process. first step involves constructing an...

This paper introduces a novel model order reduction (MOR) method for linear discrete-time systems, focusing on frequency-limited balanced truncation (BT) techniques. By leveraging Laguerre functions, we develop two efficient MOR algorithms that avoid the computationally expensive generalized Lyapunov equation solvers used in traditional methods. These employ recursive formulas to calculate expansion coefficients, which are then derive low-rank decomposition factors controllability and...

This paper introduces quadrature-based approaches that enable offline sampling of the transfer function and its derivative from available frequency response or impulse data. Unlike data-driven balanced truncation, proposed methods do not require samples function's response's derivative. Additionally, a non-intrusive approach to track error in IRKA as it refines interpolation data is presented. Furthermore, implementation equivalent ADI-based low-rank proposed. only requires at mirror images...

This paper introduces two model order-reduction techniques for second-order time-delay systems. The first method involves converting the system into a first-order form, along with set of related structure-preserving algorithms. second avoids original form and uses direct projection to produce reduced system, which can also retain structure one. key idea proposed methods is utilize low-rank Gramian approximations construct reduced-order models. Gramians are decomposed using recurrence formula...

Model order reduction (MOR) is a process of finding lower approximation the original system. In many practical applications, only certain frequency interval interest. This motivates limited model wherein reduced found whose output fits with that system within desired interval. A frequency-limited balancing-based MOR technique proposed, which yields stable models less error than existing stability-preserving techniques. The superiority proposed highlighted help numerical examples.

Frequency-weighted model order reduction techniques aim to yield a reduced whose output matches that of the original system in emphasized frequency region. However, passivity is only known be preserved single-sided weighted case. A frequency-weighted technique proposed, which guarantees passive models double-sided set easily computable error bound expressions are also presented.

A model order reduction algorithm is presented that generates a reduced-order of the original high-order model, which ensures high-fidelity within desired time interval. The reduced satisfies subset first-order optimality conditions for time-limited H$_2$-model problem. uses computationally efficient Krylov subspace-based framework to generate and it applicable large-scale systems. parameterized enforce in an iteration-free way. We also propose adaptive algorithm, monotonic decay error...

Model order reduction involves constructing a reduced-order approximation of high-order model while retaining its essential characteristics. This serves as substitute for the original one in various applications such simulation, analysis, and design. Often, there's need to maintain high accuracy within specific time or frequency interval, errors beyond this limit can be tolerated. paper addresses time-limited frequency-limited scenarios linear systems with quadratic outputs, by generalizing...

Many integrated electrical circuits and networks comprise of large RLC ladders. These complex are described by high-order positive-real transfer functions. To simplify the design analysis these systems, model reduction techniques used. It is critical importance that structure function retained in process. Moreover, it often interest reduced-order surrogate accurately approximates original system within a limited time or frequency range. In this paper, truncated balanced realizations which...

In the time- and frequency-limited model order reduction, a reduced-order approximation of original high-order is sought to ensure superior accuracy in some desired time frequency intervals. We first consider time-limited H2-optimal reduction problem for bilinear control systems derive first-order optimality conditions that local optimum should satisfy. then propose heuristic algorithm generates model, which tends achieve these conditions. The H2-pseudo-optimal problems are also considered...

Abstract The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within frequency region emphasized by weights. In this paper, we investigate $\mathcal{H}_2$-pseudo-optimal problem wherein subset optimality conditions for local optimum is attempted be satisfied. We propose two iteration-free algorithms, single-sided case $\mathcal{H}_2$-model reduction, where ensured reduced system. addition,...

In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto reduced subspace that contains its dominant characteristics. The problem frequency-weighted H2-optimal reduction to construct local optimum in terms H2-norm weighted error transfer function. this paper, algorithm proposed constructs model, which nearly satisfies first-order optimality conditions for problem. It shown as increased, deviation satisfaction...

A cross‐gramian‐based frequency‐weighted model/controller‐order reduction technique is proposed for single‐input single‐output and symmetric MIMO stable systems. The algorithm does not require the original system to be minimal. Numerical examples are presented show effectiveness of technique.

Abstract In this paper, we present an adaptive framework for constructing a pseudo‐optimal reduced model the frequency‐limited ‐optimal order reduction problem. We show that reduced‐order has inherent property of monotonic decay in error if interpolation points and tangential directions are selected appropriately. also can be used to make automatic selection allowable tolerance error. The proposed algorithm adaptively increases such ‐norm decays monotonically irrespective choice directions....

The frequency-weighted model reduction problem is of great importance in control system design due to its applications obtaining a lower order controller for significantly high plant. In this paper, two algorithms using Krylov subspace based inter-polatory framework are presented. Numerical examples presented signify the efficacy proposed algorithms.

Time limited Gramians based balanced model reduction techniques for discrete time systems are proposed. These address the stability problem of reduced order models and also yield comparable step response error bounds. Different numerical examples presented to show effectiveness proposed in desired intervals.

In this paper, a new frequency-weighted positive real balanced truncation technique is presented by using combination of model reduction with the real-truncated realization (PR-TBR). The proposed yields passive reduced-order for given high order single-sided weighting only. simulation results are shown an example problem RLC ladder network.

In this paper, a model reduction method for FIR filters with complex coefficients based on frequency interval impulse response Gramians is developed. The advantage of the proposed that only one Lyapunov equation needs to be solved in order obtain information regarding controllability and observability system. addition overcomes limitations using cross which are not applicable coefficients. effectiveness demonstrated by numerical example.

In frequency-limited model order reduction, a lower-order approximate of the high-order is sought such that it closely approximates original system within specified frequency interval. this paper, three balanced truncation algorithms are qualitatively and quantitatively compared. The pros cons each algorithm discussed. Further, noted these can be effortlessly generalized to obtain families reduction with interesting properties like stability preservation availability apriori error bound expression.

An important class of dynamical systems with several practical applications is linear quadratic outputs. These models have the same state equation as standard time-invariant but differ in their output equations, which are nonlinear functions system states. When dealing exceptionally high order, computational demands for simulation and analysis can become overwhelming. In such cases, model order reduction proves to be a useful technique, it allows constructing reduced-order that accurately...