Observers for descriptor systems

Fahmy, Mahmoud; O’Reilly, J.

doi:10.1080/00207178908961369

Cited by 17 publications

(23 citation statements)

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“…where the matrices A, E, and C are given, and X , F, and G need to be determined, naturally arises [15][16][17] in state and velocity estimation of systems of the form…”

Section: X(t) = Ax(t)+bu(t) Y = Cx(t)mentioning

confidence: 99%

A new algorithm for generalized Sylvester-observer equation and its application to state and velocity estimations in vibrating systems

Carvalho¹,

Datta

2010

Numer. Linear Algebra Appl.

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We propose a new algorithm for block-wise solution of the generalized Sylvesterobserver equation XA − F XE = GC, where the matrices A, E, and C are given, the matrices X, F , and G need to be computed, and the matrix E may be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) to the observer-Hessenberg-triangular form. It is a natural generalization of the widelyknown observer-Hessenberg algorithm for the Sylvester-observer equation : XA − F X = GC, which arises in state estimation of a standard first-order state-space control system. An application of the proposed algorithm is made to state and velocity estimations of second-order control systems modeling a wide variety of vibrating structures. For dense un-structured data, the proposed algorithm is more efficient than the recently proposed SVD-based algorithm of the authors, it is heavily composed of BLAS-3 (Level 3 Basic Linear Algebra Subprograms) operations, which make the algorithm an ideal candidate for high-performance computing.

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“…where the matrices A, E, and C are given, and X , F, and G need to be determined, naturally arises [15][16][17] in state and velocity estimation of systems of the form…”

Section: X(t) = Ax(t)+bu(t) Y = Cx(t)mentioning

confidence: 99%

A new algorithm for generalized Sylvester-observer equation and its application to state and velocity estimations in vibrating systems

Carvalho¹,

Datta

2010

Numer. Linear Algebra Appl.

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“…This is called a causal observer. Among others in [12] and [13] a design procedure for linear and impulse observable descriptor systems is presented. Less restrictive are the sufficient conditions in [18] and [31] which require the detectability of the descriptor system together with another rank assumption.…”

Section: Introductionmentioning

confidence: 99%

Design of Causal Observers for Nonlinear Descriptor Systems

Labisch

Konigorski

2014

Differential-Algebraic Equations Forum

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This contribution not only provides a new necessary and sufficient condition for causal observability of nonlinear descriptor systems but also a method to design the causal observer. The approach is based on the transformation of the descriptor system into a state-space form, the so called coupled state-space system. This description exists for all regular descriptor systems no matter if they are proper or not. If the new condition is satisfied, the coupled state-space system can be modified and can be used to design a state-space observer. It is shown, that this observer is also a causal observer for the original descriptor system. Two examples illustrate the capability of the new approach.

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“…Great efforts have been made to investigate observer design problems for descriptor systems. Many approaches have been developed for linear descriptor systems (see [5][6][7][8][9][10][11][12] and the references therein). In [6,7], some full and reduced-order observer design methods for linear descriptor systems were derived from the generalized Sylvester equation.…”

Section: Introductionmentioning

confidence: 99%

“…Many approaches have been developed for linear descriptor systems (see [5][6][7][8][9][10][11][12] and the references therein). In [6,7], some full and reduced-order observer design methods for linear descriptor systems were derived from the generalized Sylvester equation. In [13,14], a kind of generalized proportional-integral (PI) and proportionalintegral-derivative (PID) observers was proposed for linear descriptor systems.…”

Section: Introductionmentioning

confidence: 99%