In this paper, we obtain some improved reverses of Young type inequalities which were established by Burqan and Khandaqji (J. Math. Inequal. 9:113-120, 2015).
MSC: 15A45; 15A60
Considering technology limitation or device restriction in practical application, we formulate new nonlinear systems with bounded gain error, which contain switched control and impulsive control. We then investigate the exponential stability of the considered systems. Finally, the effectiveness of the proposed criteria is confirmed via an example based on Chua's oscillator.
In this paper, we propose a new system called an alternate control system with double impulses. The present system is a cyclic control system, composed of four parts in a circle: to the first and last halves of each period of the system we add different continuous controls, and at the half-period time and the end of each period of the system we add different impulses. We then investigate the exponential stability of the considered system. An example based on Chua’s circuit is provided to confirm the effectiveness of the theoretical result.
In this paper, exponential stability of nonlinear systems with impulse time window, disturbance input and bounded gain error is investigated. By means of the above result and the construction of a linear stabilizing feedback controller, another criterion of exponential stability is established. A numerical example is given to demonstrate the effectiveness of the theoretical results.
MSC: 37N35; 49N25
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