Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

Using the notion of exponential QSR-dissipativity (i.e., dissipativity with respect to a quadratic supply rate given in terms real matrices Q, S,R), this article presents necessary and sufficient conditions for stabilizability nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, stabilization closed-loop system around origin equivalent plant. Furthermore, whereas strict only SOF asymptotic stabilization, it proved be full state control. New are presented as well, along noniterative semidefinite strategy controller design. Necessary matrix inequality also introduced. Some examples illustrate usefulness proposed approach.