Finite-Time Contractively Bounded Control of Positive Linear Systems under <i>H</i>_∞ Performance and Its Application to Pest Management

Abstract

This paper investigates the finite-time contractively bounded control issue for positive linear systems under H∞ performance. The notion of H∞ finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the H∞ finite-time contractive boundedness of the considered positive systems. A state feedback finite-time contractively bounded controller design method is proposed. The corresponding sufficient condition for the existence of the desired controller is derived by using the Lyapunov function method and the matrix inequality technique. Moreover, a computable scheme for solving the controller gain is established by employing the cone complementary linearization approach. Finally, a numerical example and an application example about pest management are used to validate the effectiveness of proposed conditions.

Keywords

• finite-time contractive boundedness
• positive linear systems
• <i>H</i>_∞ performance
• cone complementary linearization