Global stabilization of nonlinear systems with a class of unmatched uncertainties. (English) Zbl 0759.93060

The paper studies global stability properties of dynamical systems described by \[ \dot x(t)=f(x,t)+\tilde\xi(x,t)+B(x,t)[\xi(x,t)+u],\;x(t_ 0)=x_ 0, \] where \(x(t)\in\mathbb{R}^ n\) denotes the state, \(u(t)\in\mathbb{R}^ n\) the control, \(\tilde\xi(x,t)\) the unmatched constraints and \(\xi(x,t)\) the matched constraints. Under the assumption of global asymptotic stability of \(\dot x(t)=f(x,t)\) and under certain unboundedness assumptions on the uncertainties of the constraints as well as of \(f\) and \(B\), the author constructs a state feedback controller \(u(x,t)\) which stabilizes the closed loop system in the large. The techniques make use of the fact that Lyapunov functions are in general not unique.


93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C10 Nonlinear systems in control theory
70K20 Stability for nonlinear problems in mechanics
93C15 Control/observation systems governed by ordinary differential equations
93D09 Robust stability
93D30 Lyapunov and storage functions
Full Text: DOI


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