1962 ◽  
Vol 50 (5) ◽  
pp. 856-865 ◽  
Author(s):  
L. Zadeh
Keyword(s):  

Author(s):  
Diego Liberati

System Theory is a powerful paradigm to deal with abstract models of real processes in such a way to be accurate enough to capture the salient underlying dynamics while keeping the mathematical tools easy enough to be manageable. Its typical approach is to describe reality via a reduced subset of ordinary differential equations (ODE) linking the variables. A classical application is the circuits theory, linking the intensive (voltage) and extensive (current) variables across and through each simplified element by means of equilibrium laws at nodes and around elementary circuits. When such relationships are linear (like in ideal capacitors, resistances, and inductors, just to stay in the circuit field), a full battery of theorems does help in understanding the general properties of the ODE system. Positive systems, quite often used in compartmental processes like reservoirs in nature and pharmacologic concentration in medical therapy, enjoy most of the properties of the linear systems, with the nonlinear constraint of non negativity. More general nonlinear systems are less easily treatable unless a simple form of nonlinearity is taken into account like the ideal characteristic of a diode in circuit theory. When the physics of the process is quite known, like in the mentioned examples, it is quite easy to identify a small number of variables whose set would fully describe the dynamics of the process, once their interrelations are properly modeled: this is the classical way to approach such a problem.


2009 ◽  
Vol 18 (05) ◽  
pp. 923-931 ◽  
Author(s):  
BRATISLAV DANKOVIĆ ◽  
SAŠA NIKOLIĆ ◽  
MARKO MILOJKOVIĆ ◽  
ZORAN JOVANOVIĆ

In this paper we define a new class of the almost orthogonal filters. These filters are a generalization of the classical orthogonal filters commonly used in the circuit theory, control system theory, signal processing and process identification. Almost orthogonal filters generate the series of almost orthogonal Legendre functions on the interval (0, ∞). They can be successfully used for the analysis, synthesis and designing of imperfect technical systems. They can also be used for approximation of arbitrary functions on (0, ∞). A new method for obtaining the models of imperfect systems is presented as well. Simulations were performed in order to validate the theoretical results and the comparison of new filters with classical filters is given.


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