scholarly journals Fault Detection of Markov Jumping Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Wei Li ◽  
Fan Jiang ◽  
Zhongqiu Wang ◽  
Gongbo Zhou ◽  
Zhencai Zhu
Keyword(s):  
Fault Detection ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Reference Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Residual Generator ◽  
Stochastic Properties ◽  
Residual Generation

In this paper, the fault detection (FD) problems of discrete-time Markov jumping linear systems (MJLSs) are studied. We first focus on the stationary MJLS. The proposed FD system consists of two steps: residual generation and residual evaluation. A new reference model strategy is applied to construct a residual generator, such that it is robust against disturbances and sensitive to system faults. The generated residual signals are then evaluated according to their stochastic properties, and a threshold is computed for detecting the occurrences of faults. The upper bound of the corresponding false alarm rate (FAR) is also given. For the nonstationary MJLS, similar results are also obtained. All the solutions are presented in the form of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the results.

Asynchronous H∞ filtering fault detection for discrete-time switched linear systems

2021 ◽  
pp. 014233122110320
Author(s):  
Jinjie Huang ◽  
Xianzhi Hao ◽  
Xiaozhen Pan
Keyword(s):  
Fault Detection ◽  
Linear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Evaluation System ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switched Linear Systems

This article studies the asynchronous H∞ filtering fault detection for discrete-time switched linear systems with mode-dependent average dwell time (MDADT). Firstly, a series of mode-dependent fault detection filters are designed, and augmented with original switched systems to construct a residual evaluation system. However, in practice, the switching of the filter often lags behind the corresponding subsystem. To deal with this, the running time of the subsystem is divided into two parts: the matched and the mismatched. Then the asynchronous switched residual evaluation system is obtained, and global uniform exponential stability (GUES) and exponential H∞ performance of asynchronous switched system are guaranteed by using μ-dependent discontinuous multi-Lyapunov functions and MDADT method. The sufficient conditions for the existence of designed filter are given in terms of linear matrix inequalities (LMIs), and parameter matrices of the designed filter and MDADT can be obtained by solving these LMIs. Finally, the effectiveness of the proposed method is demonstrated by two examples.

Stabilizing Q-Parameterized Regulator Design for Discrete-Time Switched Bimodal Systems

2011 ◽  
Vol 48-49 ◽  
pp. 1097-1100
Author(s):  
Zhi Zheng Wu
Keyword(s):  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Design Method ◽  
Synthesis Method ◽  
Switched System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Numerical Example ◽  
Stabilizing Controllers

This paper considers a regulation problem for discrete-time switched bimodal linear systems. First, a set of observer-based -parameterized stabilizing controllers for the switched system is constructed. Then, a regulator synthesis method is proposed based on solving a set of linear matrix inequalities which is derived from a regulation condition for the switched system. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design method.

scholarly journals ℋ∞Performance and Stability Analysis of Linear Systems with Interval Time-Varying Delays and Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Stochastic Parameter ◽  
Stochastic Properties ◽  
Random Change

This paper deals with the problems ofℋ∞performance and stability analysis for linear systems with interval time-varying delays. It is assumed that the parameter uncertainties are of stochastic properties to represent random change of various environments. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative criteria of the concerned systems are introduced with the framework of linear matrix inequalities (LMIs). Four numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

2003 ◽  
Vol 125 (2) ◽  
pp. 249-253 ◽  
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Alternative Approach

In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

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