Substituting the PDSF controller (37) into the augmented system (38), a resulting closed-loop system can be described as
Thus, according to Corollary 8, if there exist a scalar [alpha] > 0 and matrices [??], [??], [??] in (42), and [??] in (37) satisfying (46), system (41) with the PDSF controller is admissible.
Thus, the closed-loop descriptor system (41) with the PDSF controller (37) is admissible for all the allowable uncertainties (2) and (3).
In the next example, the PDSF control law (37) is involved for stabilizing an uncertain closed-loop descriptor system.
By involving the PDSF controller (37), we correspondingly construct a set of strict LMIs by (40).
And, a set of stabilizing PDSF gains is determined by
In a second step taken in the PdsF, he (c) formalizes the process of symbolization.
(1) That the Mathematical Model of Function is Valid to Conceive "Forms of Any Kind." In the General Introduction to PdsF, where Cassirer introduces symbolization as integration and builds the general analogy with the mathematical function, he warns his reader: this mathematical analogy "goes beyond the limits of mathematics." (72) The third volume offers more information: In fact, all our preceding inquiry has repeatedly shown us that what we call the symbolic formation of the perceptual and intuitive world does not begin with the "abstract" concept, and certainly not with one of its highest expressions, the concept of exact science.
This affirmation provides the basis for Cassirer's use of the serial form in each of the three volumes of PdsF: each form is, in its internal structure, a serial form, and it is also the basis for the "pure logic of relation" that the philosophy of symbolic form is supposed to provide and on which it is built We now have to see if, based on such an extension, it is possible to construct the structure of the system of these symbolic forms as a system of serial forms.
In the third volume of PdsF, Cassirer takes into account the progress of energetics and reaffirms the systematic meaning and value of this theory.
Once he had published the three volumes of the PdsF, and, when he could find the time, he was more involved in the clarification of the phenomenological grounds of his philosophy (the elucidation of the Ur-phenomena) than in the modeling of its systematic structure.
(a) From a Perspective Immanent to the PdsF. The structure I reconstructed presents the "complex system" of the philosophy of symbolic forms.