Global Stabilization of Incommensurate Real Order Time-Varying Nonlinear Uncertain Systems

We address the stabilization of an incommensurate class of time-varying nonlinear uncertain real order systems associated with ultimate random initial-time. New global stabilization criteria to such class of systems with bounded time-varying uncertainties are proposed by introducing an improved time-varying linear state feedback controller. The ideas of fractional comparison method and Laplace linear theory has been implemented to formulate two new distinct stabilization theorems. New results concerning verification of stabilization of such class of systems that give construction of Metzler matrix and order-dependent criteria are formulated under strong and weaker Lipschitz nonlinearity. Effectiveness of applicable theoretical result is discussed including numerical simulations to complete the demonstration.