The

The past few decades have witnessed an ever increasing research interest in the control problems that are fundamental to the switched systems. These families of systems have great practical potential in many fields, such as power systems [

It is worth mentioning that an interesting research topic named “asynchronous switching” draws much attention in recent years. It usually means that the switching of controllers has a lag to the switching of system modes, because in many practical applications, it inevitably takes some time to identify the currently operating mode of the switched system and applies a matched controller. The stability, stabilizability, and filtering problem for such an asynchronous mechanism have been well studied by allowing the Lyapunov-like function (LLF) to increase during the unmatched period between the switching mode and the controller [

In most existing literatures concerning asynchronous switching, it has been implicitly assumed that the sensors can always provide unlimited amplitude signal and therefore ignore the possible effect of the sensor nonlinearity such as [

In this technical note, we aim to investigate the asynchronous

Consider the following discrete-time switched system:

The switching signal

For each possible value of

The standard saturation function with appropriate dimensions

To deal with the asynchronous switching between switching mode and corresponding controller, we let

The stochastic variables

We use stochastic variable

In this study, a class of switching signals with ADT switching is designed when the controller is obtained. Thus, the definition of ADT is recalled.

For a switching signal

For notational brevity, we rewrite sensor model (

In this note, we are interested in designing the following dynamic output feedback controller:

In order to deal with the regional mean square stability of closed-loop systems (

Denote

Assume the nonlinear function

Define a switching level set as follows:

The level set

The purpose of this study is to design

Closed-loop systems (

Under the zero-initial condition, the controlled output satisfies

Let us start with tackling the switching level set

Consider systems (

For the convenience of manipulation, we assume the matrices

Consider the quadratic LLF:

In this work, we focus our study on the asynchronous switching by considering randomly occurring sensor nonlinearity and missing measurements when collecting the output knowledge. The saturation function, which describes the sensor nonlinearity, restricts the system state and controller state in a regional area of the state space. Since

The mean square domain of attraction could be estimated by

Compared with the results presented in [

Next, we direct our attention to the

Consider systems (

In order to simplify the proof, we only consider closed-loop system (

Because (

Next, we pay our attention to the

According to the regional

Consider switched system (

Constraint (

Conditions (

Next, we pay our attention to obtaining (

It should be noted that the conditions stated in Theorem

Consider the following steps.

Initialize index

For

Check whether the solutions satisfy (

When

Consider a discrete-time switched time-delay system (

The considered sensor model is given with parameters:

The exogenous disturbance is taken as

The probabilities are taken as

By employing Algorithm

The ellipsoid parameters are obtained as

Since we have

The mean square domain of attraction could be described as

system state:

controller state:

The switching signals generated in Figure

Asynchronous switching signals (the solid line represents the switching of the system modes and the dash-dotted line represents the switching of the controllers).

State responses under the asynchronous control (system state and controller state).

Mean square domains of attraction.

The problems of asynchronous

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

This project was jointly supported by NSFC (61203126), NSFC (61374047), and BK2012111.

_{∞}filtering for networked stochastic systems with randomly occurring sensor nonlinearities and packet dropouts