Two-degree-of-freedom tracking control design for boundary controlled distributed parameter systems using formal power series

2004 ◽  
Author(s):  
T. Meurer ◽  
M. Zeitz
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Tracking Control ◽  
Control Design ◽  
Distributed Parameter Systems ◽  
Degree Of Freedom ◽  
Distributed Parameter ◽  
Formal Power ◽  
Two Degree Of Freedom

Eigenvalues for Moderately Damped Linear Systems Determined by Eigensensitivity Analysis

1990 ◽  
Author(s):  
Robert Reiss ◽  
Bo Qian ◽  
Win Aung
Keyword(s):  
Power Series ◽  
Series Solution ◽  
Distributed Parameter Systems ◽  
Degree Of Freedom ◽  
Distributed Parameter ◽  
Finite Degree ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Quadratic Eigenvalue ◽  
Complex Valued

Abstract A new method is presented to determine approximate closed-form solutions for the complex-valued frequencies of moderately damped linearly elastic structures. The approach is equally applicable to finite degree of freedom systems and distributed parameter systems. The damping operator is split into two components, the first of which uncouples the quadratic eigenvalue equation, and the eigenvalues are expressed as a power series in the second component of the damping operator. Specific numerical examples include both finite degree of freedom and distributed parameter systems. It is shown that for moderate damping, that is, when the second component of the damping operator is small, but not negligible, the series solution truncated after quadratic terms provides an excellent approximation to the true eigenvalues.

scholarly journals On transformations of formal power series

2003 ◽  
Vol 184 (2) ◽  
pp. 369-383 ◽  
Author(s):  
Manfred Droste ◽  
Guo-Qiang Zhang
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Formal Power

scholarly journals On the Square Root of a Bell Matrix

2021 ◽  
Vol 76 (1) ◽  
Author(s):  
Donatella Merlini
Keyword(s):  
Power Series ◽  
Closed Form ◽  
Formal Power Series ◽  
Computational Method ◽  
Square Root ◽  
Riordan Arrays ◽  
Formal Power

AbstractIn the context of Riordan arrays, the problem of determining the square root of a Bell matrix $$R={\mathcal {R}}(f(t)/t,\ f(t))$$ R = R ( f ( t ) / t , f ( t ) ) defined by a formal power series $$f(t)=\sum _{k \ge 0}f_kt^k$$ f ( t ) = ∑ k ≥ 0 f k t k with $$f(0)=f_0=0$$ f ( 0 ) = f 0 = 0 is presented. It is proved that if $$f^\prime (0)=1$$ f ′ ( 0 ) = 1 and $$f^{\prime \prime }(0)\ne 0$$ f ″ ( 0 ) ≠ 0 then there exists another Bell matrix $$H={\mathcal {R}}(h(t)/t,\ h(t))$$ H = R ( h ( t ) / t , h ( t ) ) such that $$H*H=R;$$ H ∗ H = R ; in particular, function h(t) is univocally determined by a symbolic computational method which in many situations allows to find the function in closed form. Moreover, it is shown that function h(t) is related to the solution of Schröder’s equation. We also compute a Riordan involution related to this kind of matrices.

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