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.

scholarly journals Stability Analysis for a Class of Discrete-Time Nonhomogeneous Markov Jump Systems with Multiplicative Noises

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Shaowei Zhou ◽  
Xiaoping Liu ◽  
Bing Chen ◽  
Hongxia Liu
Keyword(s):  
Discrete Time ◽  
Transition Probability ◽  
Convex Polytope ◽  
Linear Matrix ◽  
Infinite Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Multiplicative Noises ◽  
Jump Systems

This paper is concerned with a class of discrete-time nonhomogeneous Markov jump systems with multiplicative noises and time-varying transition probability matrices which are valued on a convex polytope. The stochastic stability and finite-time stability are considered. Some stability criteria including infinite matrix inequalities are obtained by parameter-dependent Lyapunov function. Furthermore, infinite matrix inequalities are converted into finite linear matrix inequalities (LMIs) via a set of slack matrices. Finally, two numerical examples are given to demonstrate the validity of the proposed theoretical methods.

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 H∞Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Cheng Gong ◽  
Yi Zeng
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Singular Systems ◽  
Fuzzy Model ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Delay Dependent ◽  
Jump Systems

This paper investigates theH∞filtering problem of discrete singular Markov jump systems (SMJSs) with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition onH∞-disturbance attenuation is presented, in which both stability and prescribedH∞performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependentH∞filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.

scholarly journals Finite-TimeH∞Control for a Class of Discrete-Time Markov Jump Systems with Actuator Saturation via Dynamic Antiwindup Design

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Junjie Zhao ◽  
Jing Wang ◽  
Bo Li
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Actuator Saturation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Time Control ◽  
Saturating Actuators ◽  
Finite State ◽  
Jump Systems

We deal with 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. A controller designed for unconstrained systems combined with a dynamic antiwindup compensator is given to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. The proposed conditions allow us to find dynamic anti-windup compensator which stabilize the closed-loop systems in the finite-time sense. All these conditions can be expressed in the form of linear matrix inequalities and therefore are numerically tractable, as shown in the example included in the paper.

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.

Design of unknown input observer for discrete time nonlinear generalized Markov jump systems under fault conditions

2021 ◽  
pp. 014233122110530
Author(s):  
Zhongda Tian ◽  
Shuo Li
Keyword(s):  
Discrete Time ◽  
State Equation ◽  
Linear Matrix ◽  
Unknown Input ◽  
Unknown Input Observer ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Tunneling Diode ◽  
Novel Structure ◽  
Jump Systems

In this paper, the design problem of unknown input observer for a class of nonlinear discrete time Markov jump systems has been studied. The state equation of the system with unknown input and actuator faults is considered. The unknown input observer has a relatively novel structure and can be applied to nonlinear discrete time Markov jump systems to estimate the system state and fault at the same time. Second, the design feasibility conditions of the unknown input observer based on Lyapunov function are given. Furthermore, the conditions are transformed into a set of linear matrix inequality conditions, which can be used to solve the parameters easily by using the related software toolbox. Finally, an example of nonlinear tunneling diode circuit is given to verify the feasibility and effectiveness of the proposed method.

Dissipativity-based resilient asynchronous control for Markov jump systems with sector-bounded nonlinearities

2018 ◽  
Vol 40 (9) ◽  
pp. 2821-2830 ◽  
Author(s):  
Yujie Zhang ◽  
Xiujuan Liu ◽  
Junxia Jiang ◽  
Yongshan Xiao
Keyword(s):  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Functions ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Asynchronous Control ◽  
Controller Gain ◽  
Stochastically Stable ◽  
Dissipative Control ◽  
Jump Systems

The resilient asynchronous dissipative control problem for Markov jump systems with sector-bounded nonlinearities in the discrete-time domain are examined in this study. The jumps between the system modes and controller modes are considered to be nonsynchronous. The mode transition of the controllers is governed by a nonstationary Markov chain, which can model the asynchronous jumps to different degrees that are also mode-dependent. The nonlinear functions are assumed to belong to sector sets with arbitrary boundaries. The sector boundaries can have positive and/or negative slopes, and therefore, we cover the most general case in our approach. Using the special structure of the system and by constructing a new multiple Lyapunov function, sufficient conditions regarding the existence of desired resilient asynchronous dissipative controllers are obtained in terms of linear matrix inequalities, which ensure the closed-loop system is stochastically stable and strictly dissipative. The designed controller can tolerate additive uncertainties in the controller gain matrix, which results from controller implementations. A numerical example is presented to show the effectiveness of the proposed theoretical results.

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