State feedback for nonlinear continuous-time systems: stabilization and the creation of invariant subspaces

A theory of static state feedback for multivariable continuous-time nonlinear systems is formulated. The theory applies to systems described by differential equations of the form x(t)=f(x(t),u(t)). The basic objective is to design static state feedback compensators such that the state-space trajectory of the closed-loop system is confined within a specified subspace, and the closed-loop system is internally stable. An explicit method for designing such compensators is developed. The construction of the compensators involves only quantities directly derived from the given function f.<
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