Global Stabilization of Nonlinear Systems with Inputs Subject to Magnitude and Rate Bounds: A Parametric Optimization Approach - Solís-Daun, Julio; Suárez, Rodolfo; Álvarez-Ramírez, José (SIAM journal on control and optimization, 2000)
A bounded feedback control design approach is proposed for the global asymptotic stabilization of a class of nonlinear systems with stable free dynamics. The control inputs and their derivatives are constrained to take values on sets defined by a Cartesian product of $η $-dimensional closed balls $\mathcal{B}_{r}^{η }(p)$, which are defined by means of a p-norm and a radius vector parameter $r$. In order to derive the bounded control stabilizer, the resulting procedure implies that gains (as state-functions) are obtained from the solution to a set of c -parameterized nonlinear programming problems. In general, the resulting closed-loop system could be implicitly defined, i.e., consisting of a system of differential equations plus a set of nonlinear algebraic equations (required to compute the control). Special interest is focused on an important class of homogeneous systems that includes a class of globally asymptotically stabilizable systems by linear feedback and bilinear systems. For those systems, the problem of inputs subject to globally bounded rates is also addressed.