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.

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 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.

scholarly journals Finite-Time Stabilization for Discrete-Time Delayed Markovian Jump Systems with Partially Delayed Actuator Saturation

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Guoliang Wang ◽  
Bo Feng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Controller Design ◽  
Actuator Saturation ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Time Control ◽  
Jump Systems

The finite-time control problem of discrete-time delayed Markovian jump systems with partially delayed actuator saturation is considered by a mode-dependent parameter approach. Different from the traditionally saturated actuators, a kind of saturated actuator being partially delay-dependent is firstly proposed, where both nondelay and delay states are included and occur asynchronously. Moreover, the probability distributions of such two terms are described by the Bernoulli variable and are taken into account in the controller design. Sufficient conditions for the existence of the desired controller are presented with LMIs. Finally, a numerical example is provided to show the effectiveness and superiority of the obtained results.

scholarly journals Resilient H-infinity filtering for networked nonlinear Markovian jump systems with randomly occurring distributed delay and sensor saturation

2021 ◽  
Vol 26 (2) ◽  
pp. 187-206
Author(s):  
Venkatesan Nithya ◽  
Rathinasamy Sakthivel ◽  
Yong Ren
Keyword(s):  
Sufficient Conditions ◽  
Distributed Delay ◽  
Random Variable ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Missing Measurements ◽  
Sensor Saturation ◽  
Jump Systems ◽  
Nonlinear Markovian Jump Systems

The H∞ filtering problem for a class of networked nonlinear Markovian jump systems subject to randomly occurring distributed delays, nonlinearities, quantization effects, missing measurements and sensor saturation is investigated in this paper. The measurement missing phenomenon is characterized via a random variable obeying the Bernoulli stochastic distribution. Moreover, due to bandwidth limitations, the measurement output is quantized using a logarithmic quantizer and then transmitted to the filter. Further, the output measurements are affected by sensor saturation since the communication links between the system and the filter are unreliable and is described by sector nonlinearities. The objective of this work is to design a quantized resilient filter that guarantees not only the stochastic stability of the augmented filtering error system but also a prespecified level of H∞ performance. Sufficient conditions for the existence of desired filter are established with the aid of proper Lyapunov–Krasovskii functional and linear matrix inequality approach together with stochastic analysis theory. Finally, a numerical example is presented to validate the developed theoretical results.

Finite-Time Observer Design for a Class of Markovian Jump Systems

2012 ◽  
Vol 482-484 ◽  
pp. 949-953
Author(s):  
Cheng Yong Xiao ◽  
Wei Ming Xiang
Keyword(s):  
Finite Time ◽  
Manufacturing Systems ◽  
Estimation Error ◽  
Observer Design ◽  
Disturbance Attenuation ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Design Algorithm ◽  
Short Time ◽  
Jump Systems

Markovian jump systems are often used to model occurrence of failures and repairs in manufacturing systems. This note concerns the state estimation problem for a class of Markovian jump systems, where the Markovian jump only occurs in some short time intervals. For this class of Markovian jump systems, the boundness of estimation error deserves our investigation. By introducing the concepts of finite-time stochastic stability, an observer ensuring the estimation error bounded in a prescribed boundary is constructed and the result is extended to γ-disturbance attenuation case. A design algorithm is proposed when some parameter optimization is involved. Numerical design examples are given to illustrate the effectiveness of our results.

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