markovian jumping
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2021 ◽  
Author(s):  
Rong NIE ◽  
Wenli DU ◽  
Zhongmei LI ◽  
Zhao ZHOU ◽  
Shuping HE

Abstract This paper is concerned with the asynchronous problem for a class of Markovian jumping Lur’s system (MJLSs) via sliding mode control (SMC) in continuous-time domain. Specifically, the discrete hidden Markovian model (DHMM) is employed to describe the nonsynchronization between the controller modes and the MJLSs modes. In particular, considering the nonlinearity of MJLSs, a novel Lur’e-integral-type sliding surface is constructed. In order to ensure the finite-time stability of sliding mode dynamics and the accessibility of the specified sliding surface, the asynchronous Lur’e-type SMC law of the detector mode is presented. Finally, an example of DC motor is provided to demonstrate the effectiveness of the proposed technique.


Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2446
Author(s):  
Ruofeng Rao ◽  
Jialin Huang ◽  
Xinsong Yang

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods.


2021 ◽  
pp. 2250003
Author(s):  
Mani Kant Kumar

This paper deals with the problem of mixed [Formula: see text] and passivity performance analysis of digital filters subject to Markovian jumping parameters, external disturbances, time delays and bounds of the nonlinearity functions. By employing Lyapunov theory and matrix decomposition technique, a novel sufficient condition is established. The proposed criterion ensures that the underlying system is stochastically stable and satisfies a mixed [Formula: see text] and passivity performance index simultaneously. The obtained criterion can also be employed to solve the [Formula: see text] problem or the passivity problem in a unified framework. Moreover, the problem is formulated to obtain optimal mixed [Formula: see text] and passivity performance index of the interfered digital filters. The effectiveness and superiority of our proposed results are illustrated by three examples.


Author(s):  
Ruofeng Rao

In this paper, impulsive control on a single-species Markovian jumping ecosystem leads to a stability criterion, and the newly-obtained theorems improve the related existing results. Numerical examples illuminate the effectiveness.


2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Saravanan Shanmugam ◽  
M. Syed Ali ◽  
R. Vadivel ◽  
Gyu M. Lee

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.


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