Scalable Control Design for K-positive Linear Systems ⁎ ⁎ ⁎ This work of Kawano was supported in part by JSPS KAKENHI Grant Numbers JP19K23517 and JP21K14185.

Abstract

Systems whose state is constrained to be positive allow for computationally efficient control design. These systems guarantee forward invariance of the positive orthant, which simplifies the design of stabilizing controllers. In this paper we show that this property can be extended to a wider class of systems. We study systems that guarantee forward invariance of a generic pointed, convex, solid cone and we provide (scalable) conditions for their stability and dissipativity based on linear programming. Our results are illustrated by scalable stabilizing controller design for mass-spring systems.