On nonlinear discrete-time systems driven by Markov chains

Tejada, Arturo; González, O.R.; Gray, W. Steven

doi:10.1016/j.jfranklin.2010.02.009

Cited by 12 publications

(8 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It follows from (18) that there is at least one for which , , . Moreover, , so the Markov property of (see [29, p. 127]) implies that (19), shown at the bottom of the page, holds. To bound (19), note that only if [see (1)].…”

Section: Mss Test For Hjls's With Moore (Type 0) Output Mapsmentioning

confidence: 99%

“…Moreover, , so the Markov property of (see [29, p. 127]) implies that (19), shown at the bottom of the page, holds. To bound (19), note that only if [see (1)]. Thus, it follows from (7) that (20) Also note that , , and imply that is such that .…”

Section: Mss Test For Hjls's With Moore (Type 0) Output Mapsmentioning

confidence: 99%

“…That is, . Thus, the last factor in (19) can be written as shown in the equation immediately following (19). Further, since since is a Markov chain,the last factor in (19) can be simplified and upper bounded as shown in the third equation at the bottom of the page.…”

Section: Mss Test For Hjls's With Moore (Type 0) Output Mapsmentioning

confidence: 99%

“…Further, since since is a Markov chain,the last factor in (19) can be simplified and upper bounded as shown in the third equation at the bottom of the page. Substituting this inequality and (20) into (19) yields the inequality at the bottom of this page. Finally, substituting the latter into (18) (22), is replaced by .…”

Section: Mss Test For Hjls's With Moore (Type 0) Output Mapsmentioning

confidence: 99%

“…For each type of output map, these bounds are explicitly derived from the Markov kernels associated with the HJLS's, which completely describe the dynamics of the probability distributions of their state vectors. These, in turn, constitute Markov chains in a general metric space [19].…”

mentioning

confidence: 99%

See 4 more Smart Citations

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

Tejada

González

Gray

2013

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-In this paper, the state dynamics of a supervisor implemented with a digital sequential system are represented with a finite state machine (FSM). The supervisor monitors a symbol sequence derived from a linear closed-loop system's performance and generates a switching signal for the closed-loop system. The effect of random events on the performance of the closed-loop system is analyzed by adding an exogenous Markov process input to the FSM, and by appropriately augmenting a switched system representation of the supervisor and the closed-loop system. For this class of hybrid jump linear systems, the switching signal is, in general, a non-Markovian process, making it hard to analyze its stability properties. This is ameliorated by introducing a sufficient mean square stability test that uses only upper bounds on the onestep transition probabilities of the switching signal. These bounds are explicitly derived from a Markov kernel associated with the hybrid system model. This stability test becomes necessary and sufficient when the switching signal is Markovian. To determine tighter stability bounds, procedures to determine the upper-bound transition probability matrices when the FSM has a Moore or a Mealy type output map are presented. Two examples illustrate the applicability of the presented results.Index Terms-Finite state machine (FSM), hybrid systems, Markov chains, Markov jump systems, Markov kernel, mean square stability, stochastic systems.

show abstract