<p>This paper presents a new proportional-integral-derivative control approach for positive switched systems based on a positive proportional-integral observer. First, a positive proportional-integral observer is constructed. By using the observer state, the proportional-integral-derivative control and the corresponding integral part are designed, respectively. Using 1-norm inequality, two dynamic event-triggering conditions are established for the proportional-integral observer and proportional-integral-derivative controller, respectively. A dynamic event-triggered proportional-integral observer-based dynamic event-triggered proportional-integral-derivative controller is proposed by combining the sample state and the integral of the weighted sample output estimation error. Under the designed event-triggering conditions, an interval system with upper and lower bounds is introduced. The positivity and <i>ℓ</i>₁-gain stability are achieved by realizing the according properties of the lower and upper bound systems in terms of multiple copositive Lyapunov function, respectively. All gain matrices are designed by a matrix decomposition approach and the corresponding conditions are solved by linear programming. Finally, two examples are provided to illustrate the validity of the results.</p>