Control of nonlinear chained systems. From the Routh-Hurwitz stability criterion to time-varying exponential stabilizers

摘要

We show how any linear feedback which asymptotically stabilizes the origin of a linear integrator system of order (n-1) induces a simple continuous time-varying feedback which exponentially stabilizes the origin of a nonlinear (2, n) single-chain system. The design method is related to, and extends in the specific case of chained systems, a method developed by M'Closkey and Murray (1997) in order to transform smooth feedback stabilizers yielding slow polynomial convergence into continuous homogeneous ones which give exponential convergence.