Approach to stabilisation of continuous‐time switched positive systems

The problems of stability and stabilisation for continuous‐time switched positive linear systems (SPLSs) under arbitrary switching are investigated in this study. A common quadratic copositive Lyapunov function (CQCLF) is first proposed for stability analysis of SPLSs. It is shown that the proposed Lyapunov function for a given SPLS is less conservative than a traditional common vector‐parameterised copositive Lyapunov function. Then, sufficient conditions for the existence of CQCLF that guarantees the stability of SPLSs under arbitrary switching are derived. Based on the new stability conditions, a numerical design method of state‐feedback controllers is also given to stabilise the underlying system. Finally, a numerical example is given to demonstrate the advantages of the obtained theoretical findings.