In this study an observer-based novel design of robust control system with an estimate scheme of sensor states to accommodate extended bounded-sensor faults is proposed. The sensor faults are, in general, modeled as polytopic bounds in robust control framework and are usually given as

The problems of designing fault-tolerant control systems have attracted considerable attention. Much efforts have gone to advancing practical usage of fault-tolerant systems within the avionics industry, see [

In contrast, the passive fault-tolerant control is to exploit the inherent redundancy of the system components or to use the remaining functions of the component to design a fixed compensator so as to achieve a tolerable system performance in the presence of component faults. The designed fixed controller guarantees satisfactory system performance not merely during normal operations, but under variant fault conditions. [

This paper deals with extended bounded-sensor-faults, in which sensor faults may fall outside the presumed bounds in time varying or nonlinear manners. A passive form of observer-based controller with an integrated estimate scheme of sensor states captures the phenomena of extended bounded-sensor-faults. A basic idea of control design to extended faults of sensors in an observer-based control system relies on the

This paper is organized as follows. In Section

Consider a linear time-invariant dynamical system with sensor faults

Now, consider a state observer with control law of the following form:

The following assumptions are used for demonstrating the asymptotic stability based on Lyapunov method shown in the Theorem

The assumptions addressed above have the following interpretations:

Assumptions 1 and 2 hold. Consider the system (

If the following exist:

the matrices

the matrices

for a given matrix

then the closed-loop system

Refer to [

The overall closed-loop system (

The input-output structured block diagram of the closed-loop system (

An ordinary observer-based control system.

In the last section the asymptotic stability, based on Lyapunov method, has been shown for the system with bounded sensor faults under piecewise constant assumption. Now, a set of extended sensor faults relax the previous restrictions to not only admit bounded time varying and/or nonlinear sensor function in the vertex set,

Consider closed-loop system (

We have noticed that if the true sensor function falls within the presumed polytopic bound,

It is worth noting that, under the above assumption, the signal

This subsection defines a robust performance measure and states an important theorem on which the robust performance is established. We assume that not all state information is available and is concerned with designing a fixed structure observer-based controller to stabilize the system (

Let the constant

The system is uniformly asymptotically stable.

Subject to the assumption of zero initial condition, the controlled output

Consider the closed-loop system (

Let quadratic Lyapunov function be

The following lemma is to show that the energy of the estimated output signals by observer can be limited by some matrix inequalities, which provide an upper bound of the exogenous signal,

Given that

Before stating the main theorem for the robust

Let the

We consider the signals

It is highlighted that the

The ideas of using

Before presenting the synthesis results in the next section, a useful and important lemma will be stated for clarity.

Given

In this section according to the analyzed results shown in the last section, the observer gain,

Assume

It is followed by using the well-known Elimination Lemma stated in Lemma

Now, we can summarize the step of computation.

Find feasible solutions of

Use the computed matrices

Reconstruct control gain,

This example adopted from [

Then we solve optimization problem proposed by (

(Case no. 1): The comparison of the plant states,

(Case no. 1): True sensor functions,

The second simulation, case #2, uses the condition, which is similar to the previous case, where true sensor function

(Case no. 2): The comparison of the plant states,

(Case no. 2): True sensor functions,

The third simulation, that is, (case no. 3), is to show two sensor faults. We allow the true sensor function,

(Case no. 3): The comparison of the plant states,

(Case no. 3): The true sensor functions,

Solid-diamond line represents

This paper has developed an observer-based robust control system with an estimate scheme of sensor states against extended bounded-sensor faults. In this design, the control system not only can deal with the sensor fault in a prescribed polytopic bound but also can endure the faults outside the bound. Based on the notion of quadratic stability with a robust