Event-triggered Control of Positive Systems With State Saturation Using Linear Programming

This paper proposes the event-triggered control of positive systems with state saturation both in discrete-time and continuous-time cases. A 1-norm based event-triggered mechanism is established for positive systems. Under the event-triggered mechanism, the error term between actual and sample states is transformed into interval uncertain form. Together with the properties of saturation, the systems with state saturation are transformed into interval uncertain systems and the corresponding lower and upper bounds of the system matrices are obtained, respectively. Using a linear co-positive Lyapunov function, the event-triggered controller and the auxiliary gain matrix of the domain of attraction are designed in terms of linear programming, respectively. Then, the systems with state and input saturation are also described via interval uncertain systems. An event-triggered controller is designed and thus the closed-loop systems are positive and stable under the designed controller. Furthermore, the presented event-triggered control approach is extended to the continuous-time case. Compared to existing control approaches, the event-triggered control can reduce energy consumption and increase the practicability. Finally, several numerical examples are given to illustrate the effectiveness of the proposed design.