Globally Asymptotic Stability of Stochastic Nonlinear Systems by the Output Feedback

We address the problem of the globally asymptotic stability for a class of stochastic nonlinear systems with the output feedback control. By using the backstepping design method, a novel dynamic output feedback controller is designed to ensure that the stochastic nonlinear closed-loop system is globally asymptotically stable in probability. Our way is different from the traditional mathematical induction method. Indeed, we develop a new method to study the globally asymptotic stability by introducing a series of specific inequalities. Moreover, an example and its simulations are given to illustrate the theoretical result.

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Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

Discrete Dynamics in Nature and Society ◽

10.1155/2016/7548156 ◽

2016 ◽

Vol 2016 ◽

pp. 1-11

Author(s):

Mingzhu Song ◽

Wenwen Cheng ◽

Quanxin Zhu ◽

Hongwei Zhou ◽

Hui Wang

Keyword(s):

Nonlinear Systems ◽

Asymptotic Stability ◽

Output Feedback ◽

Output Feedback Control ◽

Lyapunov Theory ◽

Stochastic Nonlinear Systems ◽

Time Varying ◽

Globally Asymptotically Stable ◽

Globally Asymptotic Stability ◽

Theoretical Results

We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

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Stability of a Class of Stochastic Nonlinear Systems with Markovian Switching

Mathematical Problems in Engineering ◽

10.1155/2015/292794 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7

Author(s):

Xiaohua Liu ◽

Wuquan Li

Keyword(s):

Nonlinear Systems ◽

Output Feedback ◽

Closed Loop ◽

Design Method ◽

Feedback Controller ◽

Markovian Switching ◽

Stochastic Nonlinear Systems ◽

Closed Loop System ◽

Output Feedback Controller ◽

The Stability

This paper investigates the stability of a class of stochastic nonlinear systems with Markovian switching via output-feedback. Based on the backstepping design method and homogeneous domination technique, an output-feedback controller is constructed to guarantee that the closed-loop system has a unique solution and is almost surely asymptotically stable. The efficiency of the output-feedback controller is demonstrated by a simulation example.

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Fuzzy Observer-Based H 2 / H ∞ Output-Feedback Control for Stochastic Nonlinear Systems with Multiplicative Noise

Mathematical Problems in Engineering ◽

10.1155/2021/7282940 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Wenxuan Yang ◽

Ting Hou

Keyword(s):

Feedback Control ◽

Nonlinear Systems ◽

Output Feedback ◽

Multiplicative Noise ◽

Design Method ◽

Fuzzy Model ◽

Output Feedback Control ◽

Stochastic Nonlinear Systems ◽

Convex Optimization Problem ◽

Schur's Complement

A design method is established for the mixed H 2 / H ∞ output-feedback control of stochastic nonlinear systems with multiplicative noise. Firstly, using T-S fuzzy rules, we obtain a fuzzy model to approximate the original nonlinear system. Then, by Schur’s complement, the suboptimal H 2 / H ∞ output-feedback control design is transformed into a two-step convex optimization problem. A numerical example is given to show the effectiveness of the proposed method.

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Adaptive Fuzzy Output-Feedback Control Design for a Class of p-Norm Stochastic Nonlinear Systems With Output Constraints

IEEE Transactions on Circuits and Systems I Regular Papers ◽

10.1109/tcsi.2021.3063084 ◽

2021 ◽

pp. 1-13

Author(s):

Liandi Fang ◽

Shihong Ding ◽

Ju H. Park ◽

Li Ma

Keyword(s):

Feedback Control ◽

Nonlinear Systems ◽

Output Feedback ◽

Output Feedback Control ◽

Control Design ◽

Stochastic Nonlinear Systems ◽

Adaptive Fuzzy ◽

Output Constraints

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Global sampled-data output feedback stabilization for a class of switched stochastic nonlinear systems with quantized input and unknown output gain

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219862976 ◽

2019 ◽

Vol 41 (16) ◽

pp. 4511-4520

Author(s):

Yan Jiang ◽

Junyong Zhai

Keyword(s):

Nonlinear Systems ◽

Output Feedback ◽

Output Feedback Control ◽

Sampling Period ◽

Feedback Stabilization ◽

Design Parameters ◽

Stochastic Nonlinear Systems ◽

Control Input ◽

Sampled Data ◽

Data Output

This paper aims at addressing the sampled-data output feedback control problem for a class of uncertain switched stochastic nonlinear systems, whose control input is quantized by a logarithmic quantizer and the output gain cannot be precisely known. We design a compensator with the quantized information. With the help of the feedback domination approach and the backstepping design method, a sampled-data output feedback controller is constructed with appropriate design parameters and a maximum sampling period to guarantee the global exponential stability in mean square of the closed-loop system under arbitrary switching. Finally, a numerical example is given to illustrate the effectiveness of the proposed scheme.

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