New results in the global stabilization of nonlinear systems via measurement feedback with application to nonholonomic systems

We study the problem of globally stabilizing through smooth time-varying measurement feedback a wide class of time-varying uncertain nonlinear systems, consisting of a linear nominal time-varying system perturbed by nonlinear terms, model uncertainties and disturbances. The nominal time-varying system is both controllable and observable. Both the uncertainties and nonlinearities are supposed to have a lower triangular structure. We propose a step-by step design, based on splitting the system into n one-dimensional interconnected systems ∑j j = 1,...,n; assuming that for each disconnected system ∑j there exists a smooth time-varying measurement feedback stabilizing controller Cj which achieves for the closed-loop system ∑j ○ Cj, j = 1,..., n, some stability properties, we give conditions under which the interconnection of ∑j ○ Cj, j = 1,..., n, maintains the same stability properties of the disconnected systems. In general, uniform global asymptotic (not exponential) stability can be obtained. We apply these results to nonholonomic systems with uncertainties in lower triangular form.