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.
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 [10] 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 [1] 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