Mean square stability analysis of sampled-data supervisory control systems

Abstract

Testable second moment stability conditions for discrete-time supervisory control systems were recently developed using the Hybrid Jump Linear Systems (HJLS's) framework. These tests are extended here to sampled-data supervisory control systems using the new sampled-data HJLS (SD-HJLS) framework. It is shown first that the p-moment stability of SD-HJLS's equipped with ideal sample and hold operators is equivalent to that of their associated HJLS's. Then, the second moment stability analysis tools developed for HJLS's are extended to SD-HJLS's. Finally, the results are illustrated through a Monte Carlo simulation of a simple example.

Stability Analysis of Stochastic Hybrid Jump Linear Systems Using a Markov Kernel Approach

“…Unfortunately, the same arguments presented after (26) in the previous subsection show that the Markov property of cannot be used to generate a general upper bound (better than "1") for the ratio of probabilities in the last inequality. This observation together with (7) show that , can be upper bounded as follows:…”

“…To determine the effect of stochastic switching as introduced, for example, by the random occurrence of failures, a Markovian stochastic process is included as an exogenous input to the FSM. A third FSM input that could be used for plant estimation purposes can also be added as in [7], but that option is not employed in the non-estimator based supervisor considered here. These hybrid jump linear systems can be considered discrete-time piecewise deterministic Markov processes (with no reset maps) [8], [9] or simplified discrete-time stochastic hybrid systems [10].…”