Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems

ABSTRACT

This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ${\mathcal{C}}^2$ Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.

Keywords:

• Stochastic nonlinear high-order feedforward systems
• finite-time stabilisation in probability
• state feedback

Notes

1. For any given ${\mathcal{C}}^2$ function V(x), the infinitesimal generator of V(x) along stochastic nonlinear system (2(2) $$\begin{array}{c}\hfill \text{d}x=f\left(x\right)\text{d}t+g^{\top }\left(x\right)\text{d}\omega ,x\left(0\right)=x_0\in R^n,\end{array}$$(2) ) is defined as $\mathcal{L}V\left(x\right)={\left(\frac{\partial V\left(x\right)}{\partial x}\right)}^{\top }f\left(x\right)+\frac{1}{2}\text{Tr}\left\{g\left(x\right)\frac{{\partial }^{2}V\left(x\right)}{\partial x^2}{g}^{\top }\left(x\right)\right\}$, where $\frac{1}{2}\text{Tr}\left\{g\left(x\right)\frac{{\partial }^{2}V\left(x\right)}{\partial x^2}{g}^{\top }\left(x\right)\right\}$ is called the Hessian term of $\mathcal{L}$.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61273125].