A constructive methodology for estimating the stability regions of interconnected nonlinear systems

A constructive methodology for estimating the stability regions of interconnected nonlinear systems is presented. One appealing figure of the methodology is that it significantly reduces the undesirable conservativeness of the Lyapunov function approach. This constructive methodology is iterative in character and yields a sequence of estimated stability regions which is shown to be a strictly monotonic increasing sequence and yet each of the iterations lies inside the entire stability region. The methodology applies to both the scalar Lyapunov function approach and the vector Lyapunov function approach and has a sound theoretical basis. Examples are provided to illustrate the constructive methodology