Global Stabilization of a Single-Species Ecosystem with Markovian Jumping under Neumann Boundary Value via Laplacian Semigroup

Abstract

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods.

Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties

“…These systems can also be classified as a case of hybrid SSs, in which switchings are managed by a Markov chain the Ref. [1]. Mathematically, Markov jump systems are classified as random systems, in which the system matrices are randomly jumped at a series of discrete times managed by the Markov process, and in the time between these random jumps, these matrices are time-invariant.…”