Global CLF Stabilization of Systems with Control Inputs Constrained to a Hyperbox

Abstract

Our main purpose in this paper is to address the problem of synthesis of regular feedback controls for the global asymptotic stabilization (gas) of nonlinear systems with controls taking values in the $m$-dimensional $\mathbf{r}$-weighted hyperbox $\mathcal{B}_{\mathbf{r}}^{m}(\infty):=[-r_{1}^{-},r_{1}^{+}]\times\cdots\times[-r_{m}^{-},r_{m}^{+}]$. Working along the line of Artstein and Sontag's control Lyapunov function (clf) approach, we study the conditions for the gas of affine systems provided an appropriate clf is known, and propose an explicit formula for a one-parameterized family of bounded regular feedback global stabilizers. The case of scalar bounded positive feedback controls ($r^{-}=0$) is also included. Finally, the problem of designing a marginally robust control function is addressed.