State Feedback Control for Stochastic Feedforward Nonlinear Systems

Liang Liu,Ming Gao

doi:10.1155/2013/908459

Abstract

This paper considers the state feedback stabilization problem for a class of stochastic feedforward nonlinear systems. By using the homogeneous domination approach, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability. A simulation example is provided to show the effectiveness of the designed controller.

Highlights

This paper considers the state feedback stabilization problem for a class of stochastic feedforward nonlinear systems
Consider the following stochastic feedforward nonlinear systems described by dx1 = x2dt + f1 (x3, u) dt + g1T (x2, u) dω
Since the stochastic stability theory was established, the stabilization problems for stochastic lower-triangular nonlinear systems have made a great number of achievements in recent years; see, for example, [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] and the other references

Summary

Introduction

Consider the following stochastic feedforward nonlinear systems described by dx1 = x2dt + f1 (x3, u) dt + g1T (x2, u) dω, dxn−2 = xn−1dt + fn−2 (xn, u) dt + gnT−2 (xn−1, u) dω, (1). Reference [21] considered the adaptive stabilization problem for feedforward nonlinear systems with time delays by taking a nested saturation feedback. Reference [23] investigated the state and output feedback control for a class of feedforward nonlinear time-delay systems. For high-order nonlinear feedforward systems, [24] considered global stabilization problem by using the generalized adding a power integrator method and a series of nested saturation functions, [25, 26] respectively dealt with the state feedback control for this kind of systems with time delay, but all these results are limited to deterministic systems. Due to the special form of this system, there are few results on stochastic feedforward systems at present

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