Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points

This paper investigates the regional control problem of switched positive systems with multiple equilibrium points. A proportional-integral-derivative controller is designed by combining the output, the error between the state and the equilibrium point, and the difference of output. A cone is introduced to design the final stable region. Two classes of copositive Lyapunov functions are constructed to achieve the stability and regional stability of subsystems and the whole systems, respectively. Then, a novel class of observers with multiple equilibrium points is proposed using a matrix decomposition approach. The observer-based proportional-integral-derivative control problem is thus solved and all states are driven to the designed cone region under the designed controller. All conditions are formulated in the form of linear programming. The novelties of this paper lie in that: (i) A proportional-integral-derivative control framework is introduced for the considered systems, (ii) Luenberger observer is developed for the observer with multiple equilibrium points, and (iii) Copositive Lyapunov functions and linear programming are employed for the analysis and design of controller and observer. Finally, the effectiveness of the proposed design is verified via two examples.