Robust Stabilization for a Class of Nonlinear Positive Systems With Multiple Disturbances

In this article, a composite anti-disturbance control of disturbance rejection and attenuation for a class of nonlinear positive systems is proposed for the first time to achieve both positivity and stability. The disturbance observer-based control (DOBC) method is utilized to compensate for the effects of the modeled disturbances, while the L₁ control strategy is adopted to suppress the effects of the disturbances which are not compensable to satisfy the L₁ index performance. Besides, two analysis schemes of the closed-loop system are presented. The first scheme is commonly used and is easy for analysis, but it has some conservativeness. The second scheme is proposed novelly with less conservativeness, which releases the positivity constraint of disturbance estimation errors. The corresponding theorems and algorithms are proposed for necessary conditions and solutions. Finally, two examples are presented to illustrate the effectiveness of the proposed control schemes.