Robust finite-time stability and stabilisation of switched positive systems

This study is concerned with robust finite-time stability and stabilisation of a class of switched positive systems. By using the multiple linear copositive Lyapunov function approach, sufficient conditions of finite-time stability and finite-time boundedness are constructed, respectively. l₁-gain is used to analyse the disturbance attenuation performance of the systems, and a finite-time weighted l₁-gain is obtained under bounded exogenous disturbances. Then, the problem of robust finite-time stabilisation of non-autonomous systems with a weighted l₁-gain is solved. All the proposed conditions are formulated in linear programming. Finally, two illustrative examples are given to show the validity of the theoretical results.