Bumpless Transfer Control of Asynchronously Switched Linear Systems with Stochastic Mode-Dependent Sojourn-Time

This paper is devoted to the problem of the bumpless transfer control of the asynchronously switched linear systems, where the sojourn time of each mode is subject to a certain stochastic process. In contrast to the so-called conventional switched systems with dwell time (DT) or mode-dependent DT (MDT) focusing on the determination of the minimum running time of a certain mode, the stochastic mode-dependent sojourn-time (SMST) is considered, where the rest of the running time out of the fixed dwell time is subject to a random distribution. The practical and inevitable unmatched phenomenon between the detected mode and the activated mode of the system caused by the sensor delay is involved in the system modeling, unlike the conventional switched systems method that is only applicable to the ideal cases of synchronous mode switching. Under the above SMST switching signal and asynchronous phenomenon, the intractable control bump is avoided by a multistage control gains design approach, which obtains superior performance as compared to the common one-step bumpless transfer control method. The effectiveness and the advantages of the proposed bumpless transfer controller are verified via the numerical examples.