Input-to-state Stability of Nonlinear Positive Systems

  • Yan Zhao
  • Fanwei MengEmail author
Regular Papers


In this paper, input-to-state stability (ISS), as a useful tool for robust analysis, is first applied to continuous-time and discrete-time nonlinear positive systems. For continuous-time and discrete-time positive systems, some new definitions of ISS are introduced. Different from the usual ISS definitions for nonlinear systems, our ISS definitions can fully reflect the positiveness requirements of states and inputs of the positive systems. By introducing the max-separable ISS Lyapunov functions, some ISS criterions are given for general nonlinear positive systems. Based on that, the ISS criterions for linear positive systems and affine nonlinear homogeneous systems are given. Through them, the ISS properties can be judged directly from the differential and algebraic characteristics of the systems. Simulation examples verify the validity of our results.


Input-to-state stability max-separable Lyapunov functions nonlinear system positive system 


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Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesQufu Normal UniversityQufuP. R. China
  2. 2.School of Mathematical SciencesUniversity of JinanJinanP. R. China

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