Independence of estimation of domain of attraction from perturbation parameters in the nonlinear multiple time scale systems

Our research presents a method for stabilising nonlinear multiple-time-scale systems. First, a generic class of nonlinear non-affine systems is addressed, where nonlinear H-infinity controllers are replaced in the subsystems, and global and local network-small-gain theorems are proposed. Next, the controller design approach is presented with details. Previously, a similar strategy was used for singularly perturbed (two-time-scale) systems. If linearisation is applicable, a new theorem is introduced. Following that, using a general class of nonlinear multiple-time-scale systems, it is demonstrated that the application of the suggested method and the estimation of the domain of attraction are independent of the perturbation parameters’ positive values. While previous techniques for stabilising nonlinear multiple-time-scale systems are often limited to two-time-scale systems and restrict perturbation parameters to conservative ranges, altering these ranges distorts the estimated domain of attraction.