Author_Institution :
Dipt. di Informatica e Sistemistica, Universita di Roma "La Sapienza", Rome, Italy
Abstract :
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 Σj, j=1,...,n; assuming that for each disconnected system Σj there exists a smooth time-varying measurement feedback stabilizing controller Cj which achieves for the closed-loop system Σj oCj, j=1,..., n, some stability properties, we give conditions under which the interconnection of Σj oCj, 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
Keywords :
asymptotic stability; closed loop systems; controllability; nonlinear control systems; observability; time-varying systems; closed-loop system; controllability; global stabilization; measurement feedback; model uncertainties; nonholonomic systems; nonlinear systems; observability; time-varying measurement feedback; time-varying uncertain nonlinear systems; uniform global asymptotic stability; Asymptotic stability; Control systems; Convergence; Feedback; Interconnected systems; Lagrangian functions; Nonlinear systems; Robust control; Time varying systems; Uncertainty;