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 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 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.

Observer-Based H∞ Control on Nonhomogeneous Discrete-Time Markov Jump Systems

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Yanyan Yin ◽  
Peng Shi ◽  
Fei Liu ◽  
Kok Lay Teo
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Closed Loop System ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Stochastically Stable ◽  
Jump Transition ◽  
Jump Systems

This paper concerns the problem of observer-based H∞ controller design for a class of discrete-time Markov jump systems with nonhomogeneous jump parameters. A nonhomogeneous jump transition probability matrix is described by a polytope set, in which values of vertices are given. By Lyapunov function approach, under the designed observer-based controller, a sufficient condition is presented to ensure the resulting closed-loop system is stochastically stable and a prescribed H∞ performance is achieved. Finally, a simulation example is given to show the effectiveness of the developed techniques.

scholarly journals Finite-Time Control of Singular Linear Semi-Markov Jump Systems

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 8
Author(s):  
Xiaofu Ji ◽  
Xuehua Liu
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
One Dimensional ◽  
Time Control ◽  
Jump Systems

The problem of finite-time control for singular linear semi-Markov jump systems (SMJSs) with unknown transition rates is considered in this paper. By designing a new semi-positive definite Lyapunov-like function, state feedback controller design methods are given that allow closed-loop singular linear SMJSs to be regular, impulse-free and stochastically finite-time-stable without external disturbance, and stochastically finite-time bounded with external disturbance. The obtained conditions are expressed by a set of strict matrix inequalities, which can be simplified to a set of linear matrix inequalities by a one dimensional search for a scalar. Two numerical examples are given to illustrate the effectiveness of proposed method.

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.

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.

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