This study initially considers the relationship between stability radius and ‐gain of linear time‐invariant positive systems. The ‐, ‐, and ‐gains of an asymptotically stable positive system are characterised in terms of stability radii and useful bounds are derived. The authors show that the structured perturbation of a stable matrix can be regarded as a closed‐loop system with uncertainty structure represented by the unknown static output feedback. This makes it possible to relate the ‐gains in terms of closed‐form expression available for stability radii of Metzler matrices. The authors generalise the above connection for positive‐delay systems as well. Performance characterisation and computation of ‐gains are also given based on linear programming for and linear matrix inequality (LMI) for . The importance of this characterisation becomes evident when state feedback controllers are designed for regular and time‐delay systems with positivity constraints. In particular, they show that positive stabilisation with maximum stability radius for the case of can be considered as an ‐gain minimisation, which can be solved by LMI. This inherently achieves the performance criterion and establishes a link to the reported iterative convex optimisation approaches that have been developed for the cases of and . A significant result of this study is the derivation of bounds for ‐gains and the unique commonality among the optimal state feedback gain matrices in obtaining ‐gains of the stabilised system.

This paper considers the analysis of dynamic systems represented by state space models and general differential equations incorporating input derivatives. First, the connection between the class of systems with derivative inputs and singular systems is established. An elimination procedure for input derivatives is given, which transfers the derivative terms from the state equation to the output equation allowing stabilization by state feedback to be performed. Second, we consider the general differential equations with derivatives of inputs and outputs and derive an equivalent state space description in standard form, which incorporates the derivatives in the state variables. This is essential since a suitable feedback configuration should involve both input and output as well as their derivatives. We provide an appropriate state space model that allows stabilization by state feedback controller to be performed. Finally, a subclass of positive system involving input derivatives is considered as a special case. It is shown that stabilization of input derivative positive system can be achieved through its equivalent positive system in standard form using LMI. Numerical examples are included to support the theoretical results.