scholarly journals Extended Dissipative Control for Markovian Jump Time-Delayed Systems with Bounded Disturbances

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
T. Poongodi ◽  
T. Saravanakumar ◽  
Prem Prakash Mishra ◽  
Quanxin Zhu
Keyword(s):  
Transition Probabilities ◽  
Reachable Set ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Actuator Fault ◽  
Markovian Jump ◽  
Jump Time ◽  
Dissipative Control ◽  
Bounded Disturbances ◽  
Delayed System

In this work, the result of reachable set bounding and extended dissipative control synthesis of the Markovian jump time-delayed system is studied subject to stochastic actuator failures and partially known transition probabilities. Specifically, a novel actuator fault model is designed, in which the actuator fault matrix satisfies a certain probabilistic condition. Under the construction of an appropriate Lyapunov–Krasovskii functional (LKF), as well as reciprocal convex approach, Jensen’s integral inequality, and reachable set lemma, delay-dependent sufficient criteria are obtained in terms of linear matrix inequalities (LMIs) for finding an ellipsoid to bound the reachable sets of the Markovian jump time-delayed system with bounded disturbances. Finally, two numerical examples are provided to validate the effectiveness of the proposed strategy.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

Stochastic Admissibility for a Class of Nonlinear Singular Markovian Jump Systems with Time-Delay and Partially Unknown Transition Probabilities

2012 ◽  
Vol 235 ◽  
pp. 254-258 ◽  
Author(s):  
Shao Hua Long ◽  
Shou Ming Zhong
Keyword(s):  
Time Delay ◽  
Transition Probabilities ◽  
Functional Method ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Weighting Matrix ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Stochastic Admissibility

The problem of the stochastic admissibility for a class of nonlinear singular Markovian jump systems with time-delay and partially unknown transition probabilities is discussed in this note. The considered singular matrices Er(t) in the discussed system are mode-dependent. By using the free-weighting matrix method and the Lyapunov functional method, a sufficient condition which guarantees the considered system to be stochastically admissible is presented in the form of linear matrix inequalities(LMIs). Finally, a numerical example is given to show the effectiveness of the presented method.

scholarly journals Stability and Stabilization of Continuous-Time Markovian Jump Singular Systems with Partly Known Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jumei Wei ◽  
Rui Ma
Keyword(s):  
Continuous Time ◽  
Controller Design ◽  
Partial Information ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
The Stability

This paper investigates the problem of the stability and stabilization of continuous-time Markovian jump singular systems with partial information on transition probabilities. A new stability criterion which is necessary and sufficient is obtained for these systems. Furthermore, sufficient conditions for the state feedback controller design are derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals ℋ∞Control for Two-Dimensional Markovian Jump Systems with State-Delays and Defective Mode Information

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanling Wei ◽  
Mao Wang ◽  
Hamid Reza Karimi ◽  
Jianbin Qiu
Keyword(s):  
State Feedback ◽  
Transition Probabilities ◽  
Linear Time ◽  
Design Method ◽  
Transition Probability ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Markovian Jump

This paper investigates the problem ofℋ∞state-feedback control for a class of two-dimensional (2D) discrete-time Markovian jump linear time-delay systems with defective mode information. The mathematical model of the 2D system is established based on the well-known Fornasini-Marchesini local state-space model, and the defective mode information simultaneously consists of the exactly known, partially unknown, and uncertain transition probabilities. By carefully analyzing the features of the transition probability matrices, together with the convexification of uncertain domains, a newℋ∞performance analysis criterion for the underlying system is firstly derived, and then theℋ∞state-feedback controller synthesis is developed via a linearisation technique. It is shown that the controller gains can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to verify the effectiveness of the proposed design method.

scholarly journals Finite-Time H ∞ State Estimation for Markovian Jump Neural Networks with Time-Varying Delays via an Extended Wirtinger’s Integral Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Saravanan Shanmugam ◽  
M. Syed Ali ◽  
R. Vadivel ◽  
Gyu M. Lee
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jumping ◽  
Double Inequality ◽  
Markovian Jump Neural Networks

This study investigates the finite-time boundedness for Markovian jump neural networks (MJNNs) with time-varying delays. An MJNN consists of a limited number of jumping modes wherein it can jump starting with one mode then onto the next by following a Markovian process with known transition probabilities. By constructing new Lyapunov–Krasovskii functional (LKF) candidates, extended Wirtinger’s, and Wirtinger’s double inequality with multiple integral terms and using activation function conditions, several sufficient conditions for Markovian jumping neural networks are derived. Furthermore, delay-dependent adequate conditions on guaranteeing the closed-loop system which are stochastically finite-time bounded (SFTB) with the prescribed H ∞ performance level are proposed. Linear matrix inequalities are utilized to obtain analysis results. The purpose is to obtain less conservative conditions on finite-time H ∞ performance for Markovian jump neural networks with time-varying delay. Eventually, simulation examples are provided to illustrate the validity of the addressed method.

scholarly journals Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yucai Ding ◽  
Hui Liu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Reachable Set ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
State Feedback Controller ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

The problems of reachable set estimation and state-feedback controller design are investigated for singular Markovian jump systems with bounded input disturbances. Based on the Lyapunov approach, several new sufficient conditions on state reachable set and output reachable set are derived to ensure the existence of ellipsoids that bound the system states and output, respectively. Moreover, a state-feedback controller is also designed based on the estimated reachable set. The derived sufficient conditions are expressed in terms of linear matrix inequalities. The effectiveness of the proposed results is illustrated by numerical examples.

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