scholarly journals A Reduced-Order Fault Detection Filtering Approach for Continuous-Time Markovian Jump Systems with Polytopic Uncertainties

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Lihong Rong ◽  
Xiuyan Peng ◽  
Biao Zhang
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
External Disturbance ◽  
Linear Matrix ◽  
Transition Rates ◽  
Markovian Jump ◽  
Reduced Order ◽  
Order Filter ◽  
Markovian Jump Linear Systems ◽  
Jump Systems

The fault detection (FD) reduced-order filtering problem is investigated for a family of continuous-time Markovian jump linear systems (MJLSs) with polytopic uncertain transition rates, which also include the totally known and partly unknown transition rates. Then, in accordance with the convexification techniques, a novel sufficient condition for the existence of FD reduced-order filter over MJLSs with deficient transition information is obtained in terms of linear matrix inequality (LMI), which can ensure the error augmented system with the FD reduced-order filter is randomly stable. In addition, a performance index is given to enhance the robustness of the residual system against deficient transition information and external disturbance, such that the error between the fault and the residual is made as small as possible to reinforce the faults sensitivity. Finally, the effectiveness of the proposed method is substantiated with two illustrative examples.

scholarly journals Fault Detection Filter Design of Polytopic Uncertain Continuous-Time Singular Markovian Jump Systems with Time-Varying Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Yunling Shi ◽  
Xiuyan Peng
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Reduced Order ◽  
Fault Detection Filter ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Detection Filter

This paper investigates the problem of full-order and reduced-order fault detection filter (FDF) design under unified linear matrix inequality (LMI) conditions for a class of continuous-time singular Markovian jump systems (CTSMJSs) with time-varying delays and polytopic uncertain transition rates. By constructing a new Lyapunov function, sufficient conditions are firstly provided for the singular model error augmented system such that the system is stochastically admissible with an H∞ performance level γ. And then, by applying a novel convex polyhedron technique to decoupled linear matrix inequalities, the full-order and reduced-order fault detection filter parameters can be obtained within a convex optimization frame. The reduced-order fault detection filter (FDF) can not only meet the fault detection accuracy requirements of complex systems but also improve the fault detection efficiency. Finally, a DC motor and an illustrative simulation example are given to verify the feasibility and effectiveness of the proposed algorithms.

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

2021 ◽  
pp. 014233122199096
Author(s):  
Yunling Shi ◽  
Xiuyan Peng
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
Design Method ◽  
Transition Rates ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Reduced Order ◽  
Jump Systems ◽  
Stochastic Admissibility ◽  
Fault Detection Filters

This work is concerned with the problem of full-order and reduced-order fault detection filters (FDFs) design in a convex optimization frame for continuous-time singular Markov jump systems (CTSMJSs) with complexity transition rates (TRs). A novel Lyapunov function construct approach is utilized to cope with the stochastic admissibility problem for CTSMJSs with complexity TRs. In order to obtain effective full-order and reduced-order FDFs, we decoupled the inequality using the presupposed Lyapunov matrix. Owing to the use of Lyapunov stochastic admissibility theory and a novel decoupling method based on convex polyhedron technique, some sufficient conditions are obtained to guarantee that the resulting full-order and reduced-order FDFs are suitable for CTSMJSs with complexity TRs. In particular, the reduced-order FDF has the advantages of small storage space and fast detection speed compared with the full order FDF. Four illustrative examples are given to explain the effectiveness of the proposed full-order and reduced-order FDFs design method.

Finite-time observer-based control for Markovian jump systems with time-varying generally uncertain transition rates

2020 ◽  
pp. 014233122096470
Author(s):  
Mengjun Li ◽  
Xiaohang Li ◽  
Dunke Lu
Keyword(s):  
Finite Time ◽  
External Disturbance ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Transition Rates ◽  
Markovian Jump ◽  
Generally Uncertain Transition Rates ◽  
Jump Systems

This paper addresses the finite-time observer-based control for Markovian jump systems with time-varying generally uncertain transition rates. In order to estimate the states, a suitable observer is designed, in which both external disturbance and Brownian motion exist. In order to solve the complex time-varying transition rates, a quantization mechanism is raised to prove the closed-loop system and the observer error system be stable. Sufficient conditions of the existences of both the observer and the observer-based controller are derived in terms of linear matrix inequalities. Eventually, two practical examples are given to testify the correctness of the results.

scholarly journals H∞ Model Reduction of 2D Markovian Jump System with Roesser Model

2012 ◽  
Vol 6-7 ◽  
pp. 135-142
Author(s):  
Xue Song Han ◽  
Yu Bo Duan
Keyword(s):  
Model Reduction ◽  
Reduced Order Model ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Roesser Model ◽  
Markovian Jump ◽  
Order Model ◽  
Existence Of A Solution ◽  
Reduced Order ◽  
Jump Systems

This paper extends the results obtained for one-dimensional Markovian jump systems to investigate the problem of H∞model reduction for a class of linear discrete time 2D Markovian jump systems with state delays in Roesser model which is time-varying and mode-independent. The reduced-order model with the same randomly jumping parameters is proposed which can make the error systems stochastically stable with a prescribed H∞ performance. A sufficient condition in terms of linear matrix inequalitiesSubscript text(LMIs) plus matrix inverse constraints are derived for the existence of a solution to the reduced-order model problems. The cone complimentarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints. A numerical example is given to illustrate the design procedures.

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