EXPONENTIAL STABILITY FOR A CLASS OF NONLINEAR GUZMÁN FRACTIONAL-ORDER SYSTEMS

Tóm tắt

This paper introduces an efficient analytical method for ad- dressing the problem of exponential stability and stabilizability of a class of nonlinear Guzmán fractional systems. The proposed approach combines mathematical transformations with concepts from fractional calculus, providing a robust framework for the analysis of dynamic systems. Initially, sufficient conditions for ensuring the exponential stability of the system are derived using Lyapunov-based techniques and expressed in terms of strict linear matrix inequalities, which are suitable for computational implementation. Subsequently, a state-feedback control law is designed to guarantee the exponential stabilizability of the closed-loop system. Using linear matrix inequalities in both stability analysis and controller design makes the method easier to apply and understand. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the proposed strategy, confirming that the theoretical results are valid and can be applied in practice to stabilize complex non- linear fractional-order systems.