Stochastic Finite-Time Stabilization for a Class of Nonlinear Markovian Jump Stochastic Systems With Impulsive Effects

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Wu-Hua Chen ◽  
Chenghai Wei ◽  
Xiaomei Lu
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Impulsive Effects ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Feedback Controllers ◽  
Finite Time Stability ◽  
And Control ◽  
Stochastic Lyapunov Function

This paper is dedicated to the study of stochastic finite-time stability (SFTS) and control synthesis for a class of nonlinear Markovian jump stochastic systems with impulsive effects. By introducing a time-varying stochastic Lyapunov function with discontinuities at impulse times, an improved criterion for SFTS is derived in terms of linear matrix inequalities (LMIs). Based on the new SFTS criterion, four kinds of finite-time hybrid/continuous-time state feedback controllers are constructed by using the solutions to certain sets of LMIs. The effectiveness of the proposed method is validated through one numerical example.

scholarly journals Stabilization of Semi-Markovian Jump Systems with Uncertain Probability Intensities and Its Extension to Quantized Control

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Ngoc Hoai An Nguyen ◽  
Sung Hyun Kim ◽  
Jun Choi
Keyword(s):  
Markovian Jump Systems ◽  
Control Synthesis ◽  
Markovian Jump ◽  
Infinitesimal Operator ◽  
Input Quantization ◽  
Quantized Control ◽  
Stabilization Condition ◽  
Jump Systems ◽  
And Control ◽  
Stochastic Lyapunov Function

This paper concentrates on the issue of stability analysis and control synthesis for semi-Markovian jump systems (S-MJSs) with uncertain probability intensities. Here, to construct a more applicable transition model for S-MJSs, the probability intensities are taken to be uncertain, and this property is totally reflected in the stabilization condition via a relaxation process established on the basis of time-varying transition rates. Moreover, an extension of the proposed approach is made to tackle the quantized control problem of S-MJSs, where the infinitesimal operator of a stochastic Lyapunov function is clearly discussed with consideration of input quantization errors.

Stochastic Finite-Time Stability of Nonlinear Markovian Switching Systems With Impulsive Effects

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Jia Xu ◽  
Jitao Sun ◽  
Dong Yue
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Markovian Switching Systems ◽  
Linear Matrix Inequality Approach

In this paper, we introduce a new concept of stochastic finite-time stability for a class of nonlinear Markovian switching systems with impulsive effects. Based on the linear matrix inequality approach, sufficient conditions for the system to be stochastic finite-time stable are derived. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed conditions.

scholarly journals Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

scholarly journals Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xin-rong Cong ◽  
Long-suo Li
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Output Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Optimization Problem ◽  
Control Laws ◽  
The Stability ◽  
And Control

This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

Sign in / Sign up

Export Citation Format

Share Document