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  • 1
    Electronic Resource
    Electronic Resource
    Least squares completions for nonlinear differential algebraic equations (1993)
    Springer
    Numerische Mathematik 65 (1993), S. 77-94 
    Details
    ISSN: 0945-3245
    Keywords: 34A09 ; 65L05 ; 65H10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A method has been proposed for numerically solving lower dimensional, nonlinear, higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit Runge-Kutta may not be appropriate. This method is based on solving nonlinear DAE derivative arrays using nonlinear singular least squares methods. The theoretical foundations, generality, and limitations of this approach remain to be determined. This paper carefully examines several key aspects of this approach. The emphasis is on general results rather than specific results based on the structure of various applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385741
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Duality, observability, and controllability for linear time-varying descriptor systems (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 455-470 
    Details
    ISSN: 1531-5878
    Keywords: 34A08 ; 93B07 ; 93B15 ; 93C15 ; 93C50 ; Key words ; Descriptor ; Singular ; Differential-algebraic ; Observability ; Controllability ; Duality ; Structural forms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A characterization of observability for linear time-varying descriptor systemsE(t)x′(t)+F(t)x(t)=B(t)u(t), y(t)=C(t)x(t) was recently developed. NeitherE norC were required to have constant rank. This paper defines a dual system, and a type of controllability so that observability of the original system is equivalent to controllability of the dual system. Criteria for observability and controllability are given in terms of arrays of derivatives of the original coefficients. In addition, the duality results of this paper lead to an improvement on a previous fundamental structure result for solvable systems of the formE(t)x′(t)+F(t)x(t)=f(tt).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194883
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  • 3
    Electronic Resource
    Electronic Resource
    Mixed symbolic–numerical computations with general DAEs II: An applications case study (1998)
    Springer
    Numerical algorithms 19 (1998), S. 85-94 
    Details
    ISSN: 1572-9265
    Keywords: differential–algebraic equations ; DAE ; numerical integration ; implicit differential equation ; 34A09 ; 65L05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019106507166
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