The boundary crossing theorem and the zero exclusion principle are very useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.
In this work, a discrete feedback of single and a delayed time is introduced in a LTI control discrete system, yielding a monoparametric family of LTI systems. A polynomial approach technique to compute the maximal robust stability interval of the monoparametric system with single and delayed time controller is developed by using the zero exclusion principle and the boundary crossing theorem. Illustrative examples are given to show the technique.
This paper reports an analysis on proxy-based sliding mode control (PSMC), which is a controller proposed by Kikuuwe & Fujimoto (2006, Proceedings of the 2006 IEEE International Conference on Robotics and Automation, pp. 25–30) originally for position control of robot manipulators. The describing function method is employed to investigate the chattering behavior of PSMC combined with a simple second-order plant with parasitic dynamics. The results show that PSMC is capable of achieving a lower tendency to chattering than the boundary-layer implementation of sliding mode control with the same sliding surface, without affecting the insensitivity to disturbance.
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