α− dissipative filtering for Singular Markov jump system with time delays

2022 ◽  
pp. 014233122110694
Author(s):  
Juan Zhou ◽  
HuiLing Lai ◽  
Bo Men
Keyword(s):  
Time Delays ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump System ◽  
Error System ◽  
Jump Systems ◽  
Dissipative Filtering ◽  
Partitioning Technique

This paper considers the [Formula: see text] dissipative filtering problem for a class of Singular Markov jump systems (SMJSs) with distributed time delays and discrete time delays. First, using Lyapunov’s stability theory and combining delay partitioning technique, integral partitioning technique, and free weight matrix method, the sufficient conditions for stochastic admissibility and [Formula: see text] dissipation of system are studied. Then, a filtering design method based on linear matrix inequalities (LMIs) is given to make the filtering error system stochastically admissible and [Formula: see text] dissipative. Finally, numerical simulations verify the effectiveness of the resulting method.

On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval

2011 ◽  
Vol 34 (7) ◽  
pp. 841-849 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Non Linear ◽  
Robust Controllability ◽  
Jump Systems ◽  
Takagi Sugeno

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches.

An event-triggered approach to finite-time observer-based control for Markov jump systems with repeated scalar nonlinearities

2017 ◽  
Vol 40 (9) ◽  
pp. 2789-2797 ◽  
Author(s):  
Jingyu Li ◽  
Liang Shen ◽  
Fengqi Yao ◽  
Huanyu Zhao ◽  
Jing Wang
Keyword(s):  
Finite Time ◽  
Design Method ◽  
Function Technique ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Diagonally Dominant Matrix ◽  
Error System ◽  
Dominant Matrix ◽  
Jump Systems ◽  
Event Triggered

This paper studies the issue of finite-time observer-based control via an event-triggered scheme for Markov jump repeated scalar nonlinear systems. An observer-based controller via an event-triggered scheme is proposed, which can save the limited network communication bandwidth effectively, so that the resulting error system is stochastically finite-time bounded. Based on the positive definite diagonally dominant matrix and the Lyapunov function technique, a sufficient condition is presented for the solvability of the addressed problem, and the desired observer-based controller can be constructed via a convex optimization problem. In the end, a simulation example is employed to show the validity and practicability of the proposed design method.

scholarly journals Nonfragile Quantized Dissipative Filter for Nonlinear Networked Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Kewang Huang ◽  
Jianfeng Wang ◽  
Feng Pan
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Networked Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Parameter Perturbation ◽  
Filter Parameter ◽  
Performance Requirements ◽  
One Step ◽  
Error System

To address the problem of filter parameter perturbation in nonlinear networked systems, a nonfragile quantized dissipative filter is designed by considering the coexistence of random one-step time delay, multipacket losses, and quantization error. We acquired the sufficient conditions for the existence of filter by choosing appropriate Lyapunov function as well as utilizing linear matrix inequality. Furthermore, we obtained the parameter expressions of the designed filter. The designed filter could meet the performance requirements of stability and dissipativity for the filter error system under the condition of allowed time delays, packet loss probability, and quantization density. The effectiveness of the designed filter is verified by numerical simulation.

scholarly journals Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Fei Chen ◽  
Fei Liu ◽  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Space Representation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Finite Time Stabilization

This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

scholarly journals Dissipativity-based asynchronous control for discrete-time singular Markov jump systems with multiplicative noises

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141985161
Author(s):  
Xiao Lu ◽  
Jiaqiang Yan ◽  
Haixia Wang ◽  
Chunyang Sheng ◽  
Zhiguo Zhang ◽  
...  
Keyword(s):  
Discrete Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
Output Measurement ◽  
Markov Jump Systems ◽  
Multiplicative Noises ◽  
Jump Systems

The singular systems, which could widely describe more general systems and present traits of physical features, are discussed in this study. Taking the fact that noises always exist in the state and output measurement of one singular system into consideration, which may cause some errors and decrease system performance, this article devotes itself to the dissipative control for discrete-time singular Markov jump systems (SMJSs) with multiplicative noises. To deal with the asynchronous phenomena between the system modes and the controller modes, a set of Markov chains are constructed. To make sure the closed-loop singular system is dissipative, a set of sufficient conditions are derived based on the linear matrix inequalities, and then the asynchronous controller is designed to ensure that SMJSs are stochastically admissible and strictly dissipative. Finally, a simulation example is carried out to verify the correctness of the derived theorem. The designed asynchronous controller improves the robustness of the controller and overcomes the asynchronous phenomenon. This control method can be applied in the fields of robot control system.

Stochastic Finite-Time Stabilization for Uncertain Jump Systems via State Feedback

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
External Disturbances ◽  
Markov Jump Systems ◽  
Finite State ◽  
Finite Time Stabilization ◽  
Jump Systems

The stochastic finite-time stabilization problem is considered for a class of linear uncertain Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By using the appropriate stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are proposed for the design of stochastic finite-time stabilization controller. The stabilization criteria are formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The designed finite-time stabilized controller makes the stochastic MJSs stochastic finite-time bounded and stochastic finite-time stabilizable for all admissible unknown external disturbances and uncertain parameters. Simulation results illustrate the effectiveness of the developed approaches.

scholarly journals Finite-TimeH∞Control for Discrete-Time Markov Jump Systems with Actuator Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Bo Li ◽  
Junjie Zhao
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Finite Time Stability ◽  
Time Control ◽  
Jump Systems

This paper investigates the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. The finite-timeH∞controller via state feedback is designed to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic control performance of discrete-time Markov jump systems are derived in the form of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

scholarly journals RobustH∞Filtering for Discrete-Time Markov Jump Linear System with Missing Measurements

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yingjun Niu ◽  
Wei Dong ◽  
Yindong Ji
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Missing Measurements ◽  
Markov Jump ◽  
Stochastically Stable ◽  
Error System ◽  
Markov Jump Linear System

The problem of robustH∞filtering is investigated for discrete-time Markov jump linear system (DMJLS) with uncertain parameters and missing measurements. The missing measurements process is modelled as a Bernoulli distributed sequence. A robustH∞filter is designed and sufficient conditions are established in terms of linear matrix inequalities via a mode-dependent Lyapunov function approach, such that, for all admissible uncertain parameters and missing measurements, the resulting filtering error system is robustly stochastically stable and a guaranteedH∞performance constraint is achieved. Furthermore, the optimalH∞performance index is subsequently obtained by solving a convex optimisation problem and the missing measurements effects on theH∞performance are evaluated. A numerical example is given to illustrate the feasibility and effectiveness of the proposed filter.

scholarly journals ℋ∞Filter Design with Minimum Entropy for Continuous-Time Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jie Zhang ◽  
Hamid Reza Karimi ◽  
Zhong Zheng ◽  
Ming Lyu ◽  
Yuming Bo
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Design Method ◽  
State Space Model ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Minimum Entropy ◽  
Reduced Order ◽  
Error System

We deal with the design problem of minimum entropyℋ∞filter in terms of linear matrix inequality (LMI) approach for linear continuous-time systems with a state-space model subject to parameter uncertainty that belongs to a given convex bounded polyhedral domain. Given a stable uncertain linear system, our attention is focused on the design of full-order and reduced-order robust minimum entropyℋ∞filters, which guarantee the filtering error system to be asymptotically stable and are required to minimize the filtering error system entropy (ats0=∞) and to satisfy a prescribedℋ∞disturbance attenuation performance. Sufficient conditions for the existence of desired full-order and reduced-order filters are established in terms of LMIs, respectively, and the corresponding filter synthesis is cast into a convex optimization problem which can be efficiently handled by using standard numerical software. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

scholarly journals RobustH∞Filtering for a Class of Complex Networks with Stochastic Packet Dropouts and Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Zhang ◽  
Ming Lyu ◽  
Hamid Reza Karimi ◽  
Pengfei Guo ◽  
Yuming Bo
Keyword(s):  
Time Delays ◽  
Design Method ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Random Variable ◽  
Linear Matrix ◽  
Packet Dropout ◽  
Network Systems ◽  
Packet Dropouts ◽  
Delay Phenomenon

The robustH∞filtering problem is investigated for a class of complex network systems which has stochastic packet dropouts and time delays, combined with disturbance inputs. The packet dropout phenomenon occurs in a random way and the occurrence probability for each measurement output node is governed by an individual random variable. Besides, the time delay phenomenon is assumed to occur in a nonlinear vector-valued function. We aim to design a filter such that the estimation error converges to zero exponentially in the mean square, while the disturbance rejection attenuation is constrained to a given level by means of theH∞performance index. By constructing the proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the state detection observer for the discrete systems, and the observer gain is also derived by solving linear matrix inequalities. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

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