Pole assignment by state-derivative feedback for single-input linear systems

2007 ◽  
Vol 221 (7) ◽  
pp. 991-1000 ◽  
Author(s):  
T. H. S. Abdelaziz
Keyword(s):  
Linear Systems ◽  
Pole Assignment ◽  
Single Input

An algorithm for the single-input partial pole assignment problem

1998 ◽  
Vol 89 (6) ◽  
pp. 1591-1606
Author(s):  
A. Yu Yeremin ◽  
N. L. Zamarashkin ◽  
S. A. Kharchenko
Keyword(s):  
Assignment Problem ◽  
Pole Assignment ◽  
Single Input

A computational algorithm for pole assignment of linear single-input systems

1984 ◽  
Vol 29 (11) ◽  
pp. 1045-1048 ◽  
Author(s):  
P. Petkov ◽  
N. Christov ◽  
M. Konstantinov
Keyword(s):  
Computational Algorithm ◽  
Pole Assignment ◽  
Single Input

Fourier Analysis in Systems Theory

2009 ◽  
Author(s):  
Robert J Marks II
Keyword(s):  
Fourier Analysis ◽  
Systems Theory ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Homogeneous Systems ◽  
Single Output ◽  
System Operator ◽  
Single Input ◽  
Necessary And Sufficient

In the most general sense, any process wherein a stimulus generates a corresponding response can be dubbed a system. For a temporal system with single input, f (t), and single output, g(t), the relation can be written as . . . g(t) = S{ f (t)} (3.1) . . . where S{·} is the system operator. This is illustrated in Figure 3.1. There exist numerous system types. We define them here in terms of continuous signals. The equivalents in discrete time are given as an exercise. For homogeneous systems, amplifying or attenuating the input likewise amplifying or attenuating the output. For any constant, a,. . . S{a f(t)} = aS{ f (t)} (3.2) If the response of the sum is the sum of the responses, the system is said to be additive. Specifically,. . . S{ f1(t) + f2(t)} = S{ f1(t)} + S{ f2(t)} (3.3) . . . Systems that are both homogeneous and additive are said to be linear. The criteria in (3.2) and (3.3) can be combined into a single necessary and sufficient condition for linearity.. . . S{a f1(t) + bf2(t)} = aS{ f1(t)} + bS{ f2(t)} (3.4) . . . where a and b are constants. All linear systems produce a zero output when the input is zero. . . . S{0} = 0. (3.5). . . To show this, we use (3.4) with a = −b and f1(t) = f2(t). Note that, because of (3.5), the system defined by . . . g(t) = b f(t) + c . . . where b and c¹ 0 are constants, is not linear. It is not homogeneous since . . . S{a f} = b f + c ≠aS{ f} = a (b f + c) .

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