Asymmetrically scaled sectorial supply rates and asymmetric gain supply rates for semi-infinite state spaces with interior targets

This paper studies the capabilities and limitations of asymmetric gain supply rates and asymmetrically scaled sectorial (ASSEC) supply rates for analysis and design of cyclic network systems on semi-infinite state spaces with interior equilibria. The asymmetric dissipativity framework this paper pursues is to compose a Lyapunov function of a network from subsystems' storage functions defined on semi-infinite state spaces to establish stability and positivity simultaneously. For subsystems admitting ASSEC supply rates, the use of asymmetric gain supply rates can be arbitrarily conservative. Nevertheless, asymmetric gain supply rates can deal with subsystems which do not accept ASSEC supply rates. Although building the theoretical framework for ASSEC supply rates is much harder than for asymmetric gain supply rates, the finally obtained formulas are simpler, more intuitive, and the least conservative.