Stabilization Method for nth-Order ODE by Distributed Control Function

The stabilization of solutions by distributed feedback control functions for second- and third-order ordinary differential equations (ODEs) has been presented in earlier studies. The present paper extends these results to the stabilization of n-th order ODEs using a distributed control function expressed in integral form with first-order derivatives. The problem of stabilizing n-th order ODE solutions by distributed control functions is significantly more complex and nontrivial. This work introduces a method for selecting the parameter set within the distributed control function. Furthermore, the connection between palindromic polynomials, log-concavity, and stability with respect to initial conditions (Lyapunov stability) in n-th order ODEs with distributed feedback control functions is established. We use the symmetry property of palindromic polynomials.