Practical stability of continuous-time switched systems without a common equilibria and governed by a time-dependent switching signal

2011 ◽  
Author(s):  
Roman Kuiava ◽  
Rodrigo A. Ramos ◽  
Hemanshu R. Pota ◽  
Luis F. C. Alberto
Keyword(s):  
Continuous Time ◽  
Switched Systems ◽  
Time Dependent ◽  
Practical Stability ◽  
Switching Signal

Practical stability of switched systems without a common equilibria and governed by a time-dependent switching signal

2013 ◽  
Vol 19 (3) ◽  
pp. 206-213 ◽  
Author(s):  
Roman Kuiava ◽  
Rodrigo A. Ramos ◽  
Hemanshu R. Pota ◽  
Luis F.C. Alberto
Keyword(s):  
Switched Systems ◽  
Time Dependent ◽  
Practical Stability ◽  
Switching Signal

Stabilization of switched systems with time-dependent switching signal

2020 ◽  
Vol 357 (18) ◽  
pp. 13552-13568
Author(s):  
Cui-Li Jin ◽  
Rui Wang ◽  
Qing-Guo Wang
Keyword(s):  
Switched Systems ◽  
Time Dependent ◽  
Switching Signal

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

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