Cheng Dai-zhan. Fractal Sets in Control Systems[J]. Applied Mathematics and Mechanics, 1993, 14(8): 699-706.
Citation: Cheng Dai-zhan. Fractal Sets in Control Systems[J]. Applied Mathematics and Mechanics, 1993, 14(8): 699-706.

Fractal Sets in Control Systems

  • Received Date: 1992-04-30
  • Publish Date: 1993-08-15
  • In this paper the Hausdorff measure of sets of integral and fractional dimensions is introduced and applied to control systems.A new concept,namely,pseudo-self-similar set is also introduced.The existence and uniqueness of such sets are then proved,and the formula for calculating the dimension of self-similar sets is extended to the psuedo-self-similar case.Using the previous theorem,we show that the reachable set of a control system may have fractional dimensions.We hope that as a new approach the geometry of fractal sets will be a proper tool to analyze the controllability and observability of nonlinear systems.
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