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1 2009

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Designing the subsets of signals and its application in systems theory

Łozowicki A., Łozowicka-Stupnicka T., Łozowicka D.

Systems Science

2009

Vol. 35, no 1

47-55

In the paper, simplified models of signals are introduced. The set of signals belonging to the class considered is divided into abstract subsets. Every subset of signals has a representative signal of a very simple form. These representative signals are next used as simplified models of signals and they can be applied to very complicated considerations in systems theory and control theory. For example, they are applied to designing high precision, state feedback control systems. In consequence, such systems approximate (for large gain in feedback loop) the inverse operation to the plant P considered. For solving this problem, the sum of differences of state variables of system and state of control signal are taken into consideration. Based on the simplified models of signals the linear combination of the state variables of system and state of control signal (not only sum of difference) can be used. This is important if the gain in the feedback tends to infinity. A scheme of such systems is presented in the paper.