^{1, 2}

^{1, 2}

^{1, 2}

^{1}

^{2}

The problem of robust

Discrete-time Markov jump linear system (DMJLS) is an important type of stochastic hybrid system, of which the parameters jumping is governed according to a finite state Markov chain. Therefore, DMJLS has both obvious continuous and discrete dynamics and is commonly used to model problems with abrupt variations in practical engineering system structures and parameters, which may be caused by random failures or sudden violent environments changes in a wide variety of areas, such as electrical engineering, signal processing, target tracking, and multifault diagnosis (see [

Among the DMJLS state estimation methods, the interacting multiple model (IMM) method, proposed in [

On the other hand, besides the parametric uncertainties, in practical applications, the measured outputs are also usually subject to the uncertainties of randomly occurring missing phenomenon due to kinds of reasons, such as the sensor fault, external disturbance, or network data transmission loss [

Although more and more efforts have been tried on the problem of filtering with missing measurements, almost all existing results are concerned with linear system [

This paper is concerned with the problem of

The rest of the paper is organized as follows. In Section

In this paper, the notations used are standard. The subscript “

For a given probability space (

When the system is in mode

Consider the following mode-dependent

Augment the model of (

System (

Given a scalar

For real matrices

With Definitions

In this section, the performance analysis of the mode-dependent

Consider the DMJLS (

For the filtering error system, construct a stochastic mode-dependent Lyapunov function as

Therefore, with

Then,

Assume the zero initial condition

In order to design an admissible

Consider the DMJLS (

Define a transformation matrix

In order to solve the problem of parametric uncertainties in Theorem

Consider the DMJLS (

Note that (

Theorem

Consider the DMJLS (

Assume the matrices

By denoting

In this section, a numerical example is presented to demonstrate the effectiveness and the feasibility of the proposed filter. Consider the DMJLS with two subsystems and the following parameters:

The minimum value of

Measurements

The corresponding realization of the jumping mode is plotted in Figure

Jumping modes.

By setting the initial condition

The filtering error response in terms of

Figure

Minimum

In this paper, the analysis and design of robust

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by Asia Research Center in Tsinghua University 2012 Young Scholar Program.

_{∞}-consensus filtering in sensor networks with multiple missing measurements: the finite-horizon case

_{∞}filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities