extended in two main directions. In the first direction, the concept of control energy function (CEF) is proposed not only to design stabilizing feedback control laws but also to provide an estimate of the stability region of the closed-loopsystem. The CLF guarantees local stability of the closedloop- system but usually cannot provide optimal estimates of its stability region. The CEF concept is more restrict than the CLF concept. Beyond the guarantee of local stability, the CEF provides global information about limit sets and optimal estimates of stability region. The second direction is related to the fact that, in general, it is difficult to find a CLF or a CEF for many nonlinear systems. In order to overcome this problem and apply the concept of CEF for a larger class of systems, the concept of generalized control energy function (GCEF) is proposed in this paper. The GCEF allows the design of nonlinear controllers even when the derivative of the energy function is positive in some bounded regions of the state space.
control Lyapunov function; energy function; stzcabilization; nonlinear systems
