Necessary and sufficient criteria for asynchronous stabilization of Markovian jump systems

2019 ◽  
Vol 356 (3) ◽  
pp. 1468-1483 ◽  
Author(s):  
Chaoxu Guan ◽  
Zhongyang Fei ◽  
Ting Yang
Keyword(s):  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Necessary And Sufficient Criteria ◽  
Necessary And Sufficient ◽  
Jump Systems

scholarly journals Positive Observer Design for Positive Delayed Markovian Jump Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Guoliang Wang
Keyword(s):  
Sufficient Conditions ◽  
Observer Design ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Rate Matrix ◽  
Transition Rate Matrix ◽  
Independent Case ◽  
Necessary And Sufficient ◽  
Jump Systems ◽  
Positive Observer

The positive observer design problem is considered for a class of positive delayed Markovian jump systems (PDMJSs). Firstly, a necessary and sufficient condition is established to check the positivity of delayed Markovian jump systems (DMJSs). Then, necessary and sufficient conditions for PDMJSs being asymptotically mean stable are established to be independent of time delay. Based on the proposed results, sufficient conditions for the existence of the desired positive observer gains including mode-independent case are provided. Additionally, more general cases that transition rate matrix (TRM) is partially unknown or uncertain are considered, respectively. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.

scholarly journals Positivel1State-Bounding Observer Design for Positive Interval Markovian Jump Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Di Zhang ◽  
Qingling Zhang ◽  
Borong Lyu
Keyword(s):  
Linear Programming ◽  
Sufficient Conditions ◽  
Observer Design ◽  
Markovian Jump Systems ◽  
Programming Approach ◽  
Markovian Jump ◽  
Parameter Uncertainties ◽  
Positive Markovian Jump Systems ◽  
Necessary And Sufficient ◽  
Jump Systems

This paper studies the problem of positivel1state-bounding observer design for a class of positive Markovian jump systems with interval parameter uncertainties by a linear programming approach. For the first, necessary and sufficient conditions are obtained for stochastic stability andl1performance of positive Markovian jump systems by an “equivalent” deterministic positive linear system. Furthermore, based on the results obtained in this paper, sufficient conditions for the existence of the positivel1state-bounding observer are derived. The conditions can be solved in terms of linear programming. Finally, a numerical example is used to illustrate the effectiveness of the results obtained.

A diffusive representation approach toward H∞ sliding mode control design for fractional-order Markovian jump systems

2020 ◽  
pp. 095965182097525
Author(s):  
Majid Parvizian ◽  
Khosro Khandani
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Suggested Approach ◽  
Stabilizing Controller ◽  
Mode Control ◽  
Jump Systems ◽  
Diffusive Representation

This article proposes a new [Formula: see text] sliding mode control strategy for stabilizing controller design for fractional-order Markovian jump systems. The suggested approach is based on the diffusive representation of fractional-order Markovian jump systems which transforms the fractional-order system into an integer-order one. Using a new Lyapunov–Krasovskii functional, the problem of [Formula: see text] sliding mode control of uncertain fractional-order Markovian jump systems with exogenous noise is investigated. We propose a sliding surface and prove its reachability. Moreover, the linear matrix inequality conditions for stochastic stability of the resultant sliding motion with a given [Formula: see text] disturbance attenuation level are derived. Eventually, the theoretical results are verified through a simulation example.

Non-fragile H∞ SMC for Markovian jump systems in a finite-time

2021 ◽  
Author(s):  
Wenhai Qi ◽  
Yaoyao Zhou ◽  
Lihua Zhang ◽  
Jinde Cao ◽  
Jun Cheng
Keyword(s):  
Finite Time ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Jump Systems
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