Reduced-Order l2−l∞ Filter Design for a Class of Discrete-Time Nonlinear Systems with Multiple Sensor Faults

Abstract EN

The reduced-order filtering problem for a class of discrete-time smooth nonlinear systems subjectto multiple sensor faults is studied.

It is well known that a smooth complex nonlinear system can be approximatedby a Takagi-Sugeno fuzzy linear system with finite number of subsystems.

In this work, firstly, the discrete-timesmooth nonlinear system is transferred into a Takagi-Sugeno fuzzy linear system with finite number of subsystems.

Secondly, a filter with the reduced order of the original system is proposed to be designed.

Different from thetraditional assumption in which the measurement of the output is ideal, the measurement of the output is subjectto sensor faults which are described via Bernoulli processes.

By using the augmentation technique, a stochasticTakagi-Sugeno filtering error system is obtained.

For the stochastic filtering error system, the exponential stabilityand the energy-to-peak performance are investigated.

Sufficient conditions which can guarantee the exponentialstability and the l2−l∞ performance are obtained.

Then, with the proposed conditions, the design procedure of thefilter for the nonlinear system is proposed.

Finally, a numerical example is used to show the effectiveness of theproposed design methodology.