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.