Output Feedback Stabilization for Stochastic Nonholonomic Systems under Arbitrary Switching

Xianjun Liu,Dongkai Zhang,Yinghui Zhao,Ye Yue

doi:10.1155/2017/7546085

Abstract

The output feedback controllers of stochastic nonholonomic systems under arbitrary switching are discussed. We adopt an observer which can simplify the design process. The designed control laws cause the calculation of the gain parameter to be very convenient since the denominator of virtual controllers does not contain the gain parameter. Finally, an example is given to show the effectiveness of controllers.

Highlights

In recent years, switched system’s control, especially under arbitrary switching, has become an active field [1,2,3]
The global stabilization of switched systems based on arbitrary switching was given [4,5,6]
The first is the arbitrary switching mentioned in this paper

Summary

Introduction

In recent years, switched system’s control, especially under arbitrary switching, has become an active field [1,2,3]. In the past ten years, the problem of stabilization for stochastic nonholonomic systems (SNSs) received much attention. They mainly can be classified into two types. Zhang et al discussed the output feedback stabilizing controllers of SNSs whose virtual control bi contains gain parameter L [25]. This will lead to a problem where the calculation of L is very difficult, especially for n ≥ 3, since the inequalities about L were quintic. For a vector or matrix X ∈ Rn×m, XT denotes its transpose, ‖X‖ denotes the Euclidean norm, Tr{X} is its trace when X is square, and L is a stochastic differential operator [26]

Problem Formulation

Output Feedback Stabilization

A Simulation Example

Conclusions