A fast algorithm to compute the of a transfer function matrix

Bruinsma, N.; Steinbuch, M Maarten

doi:10.1016/0167-6911(90)90049-z

Cited by 245 publications

(175 citation statements)

References 5 publications

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“…In [6] and [7], a quadratically convergent method has been proposed to address the more general task of computing the H ∞ norm of a transfer function matrix. To illustrate this approach for the special case of computing µ(A), let us consider the following matrix [13]:…”

Section: B the Boyd-balakrishnan Methodsmentioning

confidence: 99%

Finding the Distance to Instability of a Large Sparse Matrix

Kreßner¹

2006

2006 IEEE Conference on Computer-Aided Control Systems Design

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Abstract-The distance to instability of a matrix A is a robust measure for the stability of the corresponding dynamical systeṁ x = Ax, known to be far more reliable than checking the eigenvalues of A. In this paper, a new algorithm for computing such a distance is sketched. Built on existing approaches, its computationally most expensive part involves a usually modest number of shift-and-invert Arnoldi iterations. This makes it possible to address large sparse matrices, such as those arising from discretized partial differential equations.

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Section: B the Boyd-balakrishnan Methodsmentioning

confidence: 99%

Finding the Distance to Instability of a Large Sparse Matrix

Kreßner¹

2006

2006 IEEE Conference on Computer-Aided Control Systems Design

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“…Efficient iterative methods are available for computing this norm [5], [6], and are based on the relationship between the singular values of H(jω) and the imaginary eigenvalues of a Hamiltonian matrix obtained from a state-space realization of H(λ) [8]. This result is then used to develop a quadratically convergent algorithm for computing the H ∞ norm of a transfer function.…”

Section: Robustness In Systems and Controlmentioning

confidence: 99%

Software for Control System Analysis and Design, Singular Value Decomposition

Dooren

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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“…Computing peak frequencies can be based on a classical algorithm for estimating the L ∞ norm of a transfer matrix G(s) = D + C(s I − A) −1 B explained in detail in [9]; see also the variations in [9,11,16]. This algorithm detects in the first place the peak frequencies Ω(K ), but may also be used to estimate secondary peaks.…”

Section: Identifying Peak Frequenciesmentioning

confidence: 99%

Second-order nonsmooth optimization for H ∞ synthesis

Bompart¹,

Noll²,

Apkarian³

2007

Numer. Math.

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The standard way to compute H ∞ feedback controllers uses algebraic Riccati equations and is therefore of limited applicability. Here we present a new approach to the H ∞ output feedback control design problem, which is based on nonlinear and nonsmooth mathematical programming techniques. Our approach avoids the use of Lyapunov variables, and is therefore flexible in many practical situations.

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A fast algorithm to compute the of a transfer function matrix

Cited by 245 publications

References 5 publications

Finding the Distance to Instability of a Large Sparse Matrix

Finding the Distance to Instability of a Large Sparse Matrix

Software for Control System Analysis and Design, Singular Value Decomposition

Second-order nonsmooth optimization for H ∞ synthesis

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