Abstract :
The authors give a necessary and sufficient condition for globally stabilizing a nonlinear system, robustly with respect to unstructured uncertainties Φ˜(u,x,t), norm-bounded for each fixed x and u. This condition requires one to find a smooth, proper, and positive definite solution V(x) of a suitable partial differential inequality depending only on the system data. A procedure, based on the knowledge of V(x), is outlined for constructing almost smooth robustly stabilizing controllers. Our approach, based on Lyapunov functions, generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization, on one hand, and H ∞-control sector conditions and input-to-state stabilization on the other.
Keywords :
H/sup /spl infin control; Lyapunov methods; asymptotic stability; control system synthesis; nonlinear control systems; robust control; uncertain systems; H/sub /spl infin//-control sector conditions; almost smooth robustly stabilizing controllers; control Lyapunov function approach; input-to-state stabilization; necessary and sufficient condition; partial differential inequality; pointwise norm-bounded uncertainties; robust stabilization; smooth proper positive definite solution; unstructured uncertainties; Control systems; Lyapunov method; Nonlinear control systems; Nonlinear systems; Robust control; Robustness; State feedback; Sufficient conditions; Uncertain systems; Uncertainty;
