چكيده به لاتين
Abstract: This thesis concerns asynchronous stabilization of switched linear systems with average dwell time. Due to direct relationship between linear system poles and characteristics, moving the poles to predetermined locations to get desired state response is a more directly and tangible method than Lyapanov based methods. In fact, by means of pole placement, a flexible straightforward compromise between switching speed, system behavior and control effort is available and a worthwhile design can be accomplished in a more directly manner. In this paper, the location of system poles is determined to achieve two important goals: avoiding system unstability and performance deterioration during unmatched times with low control effort and Adjusting the impact level of the maximum asynchronous switching delay on the minimum allowed average dwell time to achieve fast switching scheme, as far as possible. Therefore, the real parts of the closed loop subsystem poles in matched and unmatched times are limited to distinct specific negative values. To have a less conservative design the upper limit for unmatched times is closer to imaginary axis. Then, linear matrix inequalities are developed to determine state feedback controllers based on matrix similarity theorems instead of Lyapanov equation. Furthermore, using those distinct maximum values and maximum asynchronous switching delay, the switching signal with average dwell time is designed to ensure the exponential stability of the system. Finally, one example is given to demonstrate the effectiveness of the proposed design method compared to some Lyapanov based methods. The results show that, since both of the upper limits are negative, system is not allowed to be unstable during matched and unmatched times while exponential stability and desired system behavior is ensured with faster switching and much lower controller gains compared to some Lyapanov based methods. Furthermore, the minimum admissible average dwell time can be determined sensitive to asynchronous switching delay or completely insensitive to it, based on the measuring situation of the switching delay.
Keywords: Asynchronous switching, Average dwell time, Matched and Unmatched intervals, Pole placement, Stability.
