# canonical form

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## canonical form

[kə′nän·ə·kəl ‚fȯrm]
(control systems)
A specific type of dynamical system representation in which the associated matrices possess specific row-column structures.
(organic chemistry)
A resonance structure for a cyclic compound in which the bonds do not intersect.
(science and technology)
A particularly clean and simple representation which usually follows or satisfies a general rule.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In the canonical form (z = 1) of the fundamental fractal F, shorter continued fractions correspond with more stable eigenstates of a chain system of harmonic oscillators.
The written canonical form of equations (2) together with the weight functions  for control the quality of the robust stabilization system, allows in the Robust Control Toolbox to calculate the transfer function of the [H.sub.[infinity]]-suboptimal regulator for the nominal object.
Shavarovskii, "On invariants and canonical form of matrices of second order with respect to semiscalar equivalence," Buletinul Academiei de Stiinfe a Republicii Moldova.
(22) into a symmetric canonical form of a double confluent Heun's equation [27, 43-45].
A LODE [[DELTA].sub.n][y] = 0 has a maximal symmetry algebra if and only if it is iterative  or, equivalently [1, 2], if and only if it can be reduced by a point transformation to the canonical form [y.sup.(n)] = 0.
where J is a matrix in Jordan canonical form and N is a nilpotent matrix also in Jordan canonical form.
Let n > 1 be an integer of canonical form n = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
reduces Equation (5) to its simplest canonical form (See Appendix 1 for full details), written here as:
Some classes enable defining a canonical form of expressions.
Figure 2(a) shows the coupling matrix in folded canonical form for a bandstop filter with equiripple rejection inside the stopband of 32 dB, N = 4 and reflection zeros at [+ or -]2.5 rad/s.
It is known (Patton, 1994; Zhirabok, 2010) that the observer can be built in the canonical form with matrices

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