On design of fault detection filter for nonlinear Markovian jump systems with sensor saturations

This paper addresses the fault detection problem for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities, randomly varying nonlinearities and sensor saturations. An optimized fault detection filter is designed such that 1) the fault detection dynamics is stochastically stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized H∞-norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized H∞-norm. The characterization of the gains of the desired fault detection filters is derived in terms of the solution to a convex optimization problem. Finally, a simulation example is employed to show the effectiveness of the scheme proposed in this paper.

[1]  Li Ma,et al.  Exponential $H_{\infty}$ Filter Design for Discrete Time-Delay Stochastic Systems With Markovian Jump Parameters and Missing Measurements , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Daniel W. C. Ho,et al.  Fuzzy Filter Design for ItÔ Stochastic Systems With Application to Sensor Fault Detection , 2009, IEEE Transactions on Fuzzy Systems.

[3]  Zehui Mao,et al.  Fault-tolerant control for a class of nonlinear sampled-data systems via a Euler approximate observer , 2010, Autom..

[4]  Yongqiang Wang,et al.  A New Fault Detection Scheme for Networked Control Systems Subject to Uncertain Time-Varying Delay , 2008, IEEE Transactions on Signal Processing.

[5]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[6]  E. Boukas,et al.  H∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities , 2009 .

[7]  Fuwen Yang,et al.  Set-membership filtering for systems with sensor saturation , 2009, Autom..

[8]  Steven X. Ding,et al.  Optimal fault detection for linear discrete time-varying systems , 2010, Autom..

[9]  Fuchun Sun,et al.  Design of reduced-order H∞ filter for Markovian jumping systems with time delay , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[10]  Zongli Lin,et al.  Robust filtering for discrete-time systems with saturation and its application to transmultiplexers , 2004, IEEE Transactions on Signal Processing.

[11]  Daniel W. C. Ho,et al.  Robust ${\cal H}_{\infty}$ Finite-Horizon Control for a Class of Stochastic Nonlinear Time-Varying Systems Subject to Sensor and Actuator Saturations , 2010, IEEE Transactions on Automatic Control.

[12]  João Yoshiyuki Ishihara,et al.  Information filtering and array algorithms for discrete-time Markovian jump linear systems , 2007, 2007 American Control Conference.

[13]  Zheng Yufan,et al.  Nonlinear H ∞ filtering for interconnected Markovian jump systems , 2006 .

[14]  J. Lam,et al.  Fixed-Order Robust Filter Design for Markovian Jump Systems With Uncertain Switching Probabilities , 2006 .

[15]  Donghua Zhou,et al.  Robust fault detection for networked systems with communication delay and data missing , 2009, Autom..

[16]  Torsten Jeinsch,et al.  A unified approach to the optimization of fault detection systems , 2000 .