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.

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 Observer Design for Delayed Markovian Jump Systems with Output State Saturation

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Guoliang Wang ◽  
Bo Feng
Keyword(s):  
Probability Distributions ◽  
Sufficient Conditions ◽  
Observer Design ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Output State ◽  
System Output ◽  
Delay Dependent ◽  
Jump Systems ◽  
State Saturation

This paper considers the observer design problem of continuous-time delayed Markovian jump systems with output state saturation. Different from the traditionally observer-based saturation control methods, a kind of system output state saturation with a partially delay-dependent property is proposed, where both nondelay and delay states exist at the same time but happen asynchronously. By exploiting the Bernoulli variable, the probability distributions of such two states are described and considered in the observer design. Based on an improved equality applied to deal with saturation terms, sufficient conditions for the designed observer with three kinds of output saturations are all provided with LMI forms. Finally, a numerical example is given to indicate the effectiveness of the obtained results.

scholarly journals Robust Stabilization of Stochastic Markovian Jump Systems with Distributed Delays

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guilei Chen ◽  
Zhenwei Zhang ◽  
Chao Li ◽  
Dianju Qiao ◽  
Bo Sun
Keyword(s):  
Linear Matrix Inequalities ◽  
Robust Stabilization ◽  
Distributed Delays ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Parameter Uncertainties ◽  
Delay Dependent ◽  
Jump Systems

This paper addresses the robust stabilization problem for a class of stochastic Markovian jump systems with distributed delays. The systems under consideration involve Brownian motion, Markov chains, distributed delays, and parameter uncertainties. By an appropriate Lyapunov–Krasovskii functional, the novel delay-dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities. When given linear matrix inequalities are feasible, an explicit expression of the desired state feedback controller is given. The designed controller, based on the obtained criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system. The convenience of the design is greatly enhanced due to the existence of an adjustable parameter in the controller. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed theory.

scholarly journals Stochastic Stability for Time-Delay Markovian Jump Systems with Sector-Bounded Nonlinearities and More General Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Dan Ye ◽  
Quan-Yong Fan ◽  
Xin-Gang Zhao ◽  
Guang-Hong Yang
Keyword(s):  
Time Delay ◽  
Stochastic Stability ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Sufficient Conditions ◽  
Transition Probability Matrix ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Delay Dependent ◽  
Jump Systems

This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs) with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.

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