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Victor Sreeram - One of the best experts on this subject based on the ideXlab platform.

  • Model Reduction via Generalized Frequency Interval Cross Gramian
    IFAC-PapersOnLine, 2020
    Co-Authors: Deepak Kumar, Victor Sreeram
    Abstract:

    Abstract In this paper, a new model reduction technique based on the generalized limited Frequency Interval cross Gramian is developed for continuous linear time invariant systems. The proposed technique is not only applicable to unstable systems but can also be applied to the systems which contain eigenvalues of opposite polarities and equal magnitude. The standard cross Gramian is generalized for such systems by transforming the system matrix of the original system using a Riccati equation.

  • Frequency Interval model reduction of complex fir digital filters
    Numerical Algebra Control and Optimization, 2019
    Co-Authors: Ahmad Jazlan, Victor Sreeram, Roberto Togneri, Umair Zulfiqar, Deepak Kumar, Hasan Firdaus Mohd Zaki
    Abstract:

    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 method is that only one Lyapunov equation needs to be solved in order to obtain the information regarding the Frequency Interval controllability and observability of the system. In addition this method overcomes the limitations of using cross Gramians which are not applicable for filters with complex coefficients. The effectiveness of the proposed method is demonstrated by a numerical example.

  • Model Reduction Using Parameterized Limited Frequency Interval Gramians for 1-D and 2-D Separable Denominator Discrete-Time Systems
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2018
    Co-Authors: Deepak Kumar, Victor Sreeram, Xin Du
    Abstract:

    In this paper, we propose model reduction algorithms based on the Frequency-domain Interval Gramians for 1-D and separable denominator 2-D discrete-time systems using balanced truncation as a parameterized combination of unweighted and the limited-Frequency Interval Gramians. The values of free parameters are computed using a line search optimization. The proposed algorithms provide a substantial improvement in the approximation error than the well-known existing techniques and generate stable reduced models along with an easily computable error-bound. The effectiveness of proposed algorithms is validated with the help of numerical examples of a sixth-order elliptic low-pass filter and a (6, 6)-order Roesser model of a separable denominator 2-D system.

  • Frequency Interval cross gramians for linear and bilinear systems
    Asian Journal of Control, 2017
    Co-Authors: Hamid Reza Shaker, Ahmad Jazlan, Victor Sreeram, Roberto Togneri, Ha Binh Minh
    Abstract:

    In many control engineering problems, it is desired to analyze the systems at particular Frequency Intervals of interest. This paper focuses on the development of Frequency Interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the Frequency Interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses Frequency Interval cross gramians relative to existing methods.

  • AuCC - Generalized gramian based Frequency Interval model reduction for unstable systems
    2016 Australian Control Conference (AuCC), 2016
    Co-Authors: Ahmad Jazlan, Victor Sreeram, Roberto Togneri, Ha Binh Minh
    Abstract:

    Frequency Interval controllability and observability gramian matrices are important in order to understand the characteristics of systems which are inherently Frequency dependent. Obtaining these Frequency Interval controllability and observability gramian matrices requires solving a pair of Lyapunov equations. However for certain systems these Lyapunov equations are not solvable. In addition the eigenvalues of the product of the Frequency Interval controllability and observability gramians may also be complex numbers and therefore these gramians are not applicable to used in the context of model reduction. To overcome these issues, generalized Frequency Interval controllability and observability gramians are introduced in this paper and the applicability of these generalized gramians to be used in model reduction is demonstrated.

Xin Du - One of the best experts on this subject based on the ideXlab platform.

  • Model Reduction Using Parameterized Limited Frequency Interval Gramians for 1-D and 2-D Separable Denominator Discrete-Time Systems
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2018
    Co-Authors: Deepak Kumar, Victor Sreeram, Xin Du
    Abstract:

    In this paper, we propose model reduction algorithms based on the Frequency-domain Interval Gramians for 1-D and separable denominator 2-D discrete-time systems using balanced truncation as a parameterized combination of unweighted and the limited-Frequency Interval Gramians. The values of free parameters are computed using a line search optimization. The proposed algorithms provide a substantial improvement in the approximation error than the well-known existing techniques and generate stable reduced models along with an easily computable error-bound. The effectiveness of proposed algorithms is validated with the help of numerical examples of a sixth-order elliptic low-pass filter and a (6, 6)-order Roesser model of a separable denominator 2-D system.

  • Balanced Truncation of Linear Time-Invariant Systems over Finite-Frequency Ranges
    arXiv: Systems and Control, 2016
    Co-Authors: Xin Du, Peter Benner
    Abstract:

    This paper discusses model order reduction of LTI systems over limited Frequency Intervals within the framework of balanced truncation. Two new \emph{Frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type Frequency-dependent balanced truncation} to copy with the cases that only a single dominating point of the operating Frequency Interval is pre-known, the other is \emph{Interval-type Frequency-dependent balanced truncation} to deal with the cases that both of the upper and lower bound of Frequency Interval are known \emph{a priori}. SF-type error bound and Interval-type error bound are derived for the first time to estimate the desired approximation error over pre-specified Frequency Interval. We show that the new methods generally lead to good in-band approximation performance, at the same time, provide accurate error bounds under certain conditions. Examples are included for illustration.

  • Model reduction of linear time delay systems via a class of balanced truncation
    Proceedings of the 32nd Chinese Control Conference, 2013
    Co-Authors: Xin Du, Chao Wang, Kun Tu
    Abstract:

    This paper investigates the model order reduction problems for linear time-delay systems with known operating Frequency Interval. Firstly, a class of linear system model which match the linear time-delay model exactly at the middle Frequency. Then, a new middle Frequency dependent balanced truncation algorithm was developed. The obtained reduced model approximate the original high-order model very well at the middle Frequency and the Frequency Interval nearby, and the error bound at the middle Frequency also established. Furthermore, the stability-preserving design conditions also derived . Finally, a numerical example was carried out to illustrate the effectiveness and advantages.

  • An LMI approach to H∞ model reduction of linear discrete-time systems over finite Frequency Interval
    2011 Chinese Control and Decision Conference (CCDC), 2011
    Co-Authors: Xin Du, Guanghong Yang, Dan Ye
    Abstract:

    In this paper, we address the finite-Frequency H∞ model reduction problem for linear time-invariant discrete-time systems. Different from the existing methods in the literature, we resort to the aid of recently developed Generalized Kalman-Yakubovich-Popov (GKYP) lemma. Based on in-depth exploitation of GKYP lemma and Projection lemma, sufficient conditions for the finite Frequency H∞ model reduction problems are derived and expressed in terms of solutions to a set of linear matrix inequalities (LMIs) which can be handled easily by using the available toolbox. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting.

  • h model reduction of linear continuous time systems over finite Frequency Interval
    Iet Control Theory and Applications, 2010
    Co-Authors: Xin Du, Guanghong Yang
    Abstract:

    This article studies the H∞ model reduction problem for linear continuous-time systems over a finite-Frequency Interval. Different from the existing methods in the literature, we resort to the aid of recently developed generalised Kalman–Yakubovich–Popov (GKYP) lemma. Based on a in-depth exploitation of the GKYP lemma and the Projection lemma, sufficient conditions for the finite-Frequency H∞ model reduction problems are derived and expressed in terms of solutions to a set of linear matrix inequalities (LMIs), which can be handled easily by using the available toolbox. Numerical examples are included for illustration.

Abdul Ghafoor - One of the best experts on this subject based on the ideXlab platform.

  • A New Frequency-Limited Interval Gramians-Based Model Order Reduction Technique
    IEEE Transactions on Circuits and Systems II: Express Briefs, 2017
    Co-Authors: Umair Zulfiqar, Abdul Ghafoor, Muhammad Imran, Muwahida Liaquat
    Abstract:

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

  • Model reduction of descriptor systems using Frequency limited Gramians
    Journal of the Franklin Institute, 2015
    Co-Authors: Muhammad Ali Imran, Abdul Ghafoor
    Abstract:

    Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole Frequency range. However, some applications require approximation over a certain band of Frequency than whole Frequency range. Different model reduction techniques are available for descriptor systems. However, for limited Frequency Interval, no such work exists in the literature. A Frequency limited balanced truncation method for general descriptor systems is proposed. The method is an extension of truncated balanced realization method for the general descriptor system. The proposed technique generalizes the results of Gawronski and Juang technique for large-scale descriptor systems using Frequency Interval Gramians. Simple algorithms are also given for preserving the stability of reduced-order models. The work also extends Poor Man's truncated balanced realization technique to include Frequency limited Gramians for descriptor systems. Practical numerical examples are incorporated to show the successful application of the proposed method in the desired Frequency range.

  • Limited Frequency Interval Gramian-based model reduction for generalised non-singular discrete time systems
    IET Control Theory & Applications, 2015
    Co-Authors: Muhammad Imran, Abdul Ghafoor, Victor Sreeram
    Abstract:

    A limited Frequency Interval Gramians-based model reduction technique for generalised non-singular discrete time systems is presented. The technique generalises the results of existing limited Frequency Interval Gramians-based model reduction (of discrete time systems) schemes to general non-singular discrete time systems. Numerical examples are also presented to illustrate the proposed technique.

  • AuCC - Limited Frequency Interval Gramians based model reduction for nonsingular generalized systems
    2013 Australian Control Conference, 2013
    Co-Authors: Muhammad Imran, Abdul Ghafoor, Safia Akram, Victor Sreeram
    Abstract:

    Limited Frequency Interval Gramians based model reduction technique for generalized nonsingular systems is presented. The technique extends results of existing limited Frequency Interval Gramians schemes for standard systems. Numerical examples are also included.

  • Limited Frequency Interval Gramians based model reduction for nonsingular generalized systems
    2013 Australian Control Conference, 2013
    Co-Authors: Muhammad Imran, Abdul Ghafoor, Safia Akram, Victor Sreeram
    Abstract:

    Limited Frequency Interval Gramians based model reduction technique for generalized nonsingular systems is presented. The technique extends results of existing limited Frequency Interval Gramians schemes for standard systems. Numerical examples are also included.

Hamid Reza Shaker - One of the best experts on this subject based on the ideXlab platform.

  • ROCOND - Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems
    IFAC Proceedings Volumes, 2020
    Co-Authors: Hamid Reza Shaker
    Abstract:

    Abstract The notions of controllability and observability play an important role in different problems within feedback control analysis and design. To verify the controllability and observability of a system, several techniques have been introduced. However, often it is not only important to verify if the system is controllable or observable, but also it is required to know the degree of controllability or observability of the system. Gramian matrices were introduced to address this issue by providing a quantitative measure for controllability and observability. In many applications, the information on the controllability and observability properties of a system is needed within a specific Frequency Interval rather than the whole Frequency-domain. The Frequency Interval gramians provide such information. While this concept were originally introduced for fixed known systems, it needs to be investigated for the case of uncertain systems. In this paper, we derive upper and lower bounds of Frequency Interval gramians under perturbations of an A -matrix in the state-space form. These bounds are obtained by solving algebraic Riccati equations. The results are further used to obtain upper and lower bounds of the Frequency Interval Hankel singular values for perturbed systems.

  • CDC - Generalized Frequency-Interval balanced model reduction method
    52nd IEEE Conference on Decision and Control, 2020
    Co-Authors: Hamid Reza Shaker
    Abstract:

    In this paper, a new method for model reduction of bilinear systems is presented. The method is developed in particular for many applications in which one is interested to approximate a system in a given Frequency-Interval. To this end, new generalized Frequency-Interval gramians are introduced for bilinear systems. It is shown that these gramians are the solutions to the so-called Frequency-Interval generalized Lyapunov equations. Algorithms are proposed to solve such equations iteratively. The method is further illustrated with the help of an illustrative example. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians.

  • On the existence of Frequency-Interval gramians for bilinear systems
    European Journal of Control, 2017
    Co-Authors: Hamid Reza Shaker, Maryamsadat Tahavori
    Abstract:

    Abstract It is well-known that gramians are specific matrices which show the degree of controllability and observability. Therefore gramians are very popular in applications such as model reduction and control configuration selection. The Frequency-Interval controllability and observability gramians have been recently introduced for bilinear systems as the solutions to the generalized Frequency-Interval Lyapunov equations. Analogous to ordinary gramians for bilinear systems, it might happen that the Frequency-Interval Lyapunov equations have unique solutions which are not controllability and observability gramians of the bilinear systems. In other words, solvability of the Frequency-Interval Lyapunov equations does not guarantee the existence of the Frequency-Interval gramians. In this paper, the conditions which are required for the existence of Frequency-Interval gramians are obtained. Further, to cope with the problem of the existence of gramians, a scaling-based method is proposed. A proof for the theorem which suggests an iterative scheme for computing the Frequency-Interval generalized gramians is also presented in this paper.

  • Frequency Interval cross gramians for linear and bilinear systems
    Asian Journal of Control, 2017
    Co-Authors: Hamid Reza Shaker, Ahmad Jazlan, Victor Sreeram, Roberto Togneri, Ha Binh Minh
    Abstract:

    In many control engineering problems, it is desired to analyze the systems at particular Frequency Intervals of interest. This paper focuses on the development of Frequency Interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the Frequency Interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses Frequency Interval cross gramians relative to existing methods.

  • Frequency Interval balanced truncation of discrete-time bilinear systems
    Cogent engineering, 2016
    Co-Authors: Ahmad Jazlan, Hamid Reza Shaker, Victor Sreeram, Roberto Togneri
    Abstract:

    This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular Frequency Intervals of interest. In order to analyze the degree of controllability and observability of discrete-time bilinear systems with emphasis on particular Frequency Intervals of interest, new generalized Frequency Interval controllability and observability gramians are introduced in this paper. These gramians are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new generalized Frequency Interval controllability and observability gramians as part of the balanced truncation framework ...

Guanghong Yang - One of the best experts on this subject based on the ideXlab platform.