Dissipativity analysis and synthesis of discrete-time T-S fuzzy stochastic systems

Dissipativity theory has played a critical part in the analysis and control design of linear and nonlinear systems, especially for high-order systems, since from the practical application point of view, many systems need to be dissipative for achieving effective noise attenuation [51]. It has been recognized that for more abstract systems one can still associate them with an energylike function (called the storage function) and an input-power-like function (called the supply rate). Dissipativity is then characterized by storage functions and supply rates, which represent the energy stored inside the system and energy supplied from outside the system, respectively. Generally speaking, dissipative systems are those for which the increase in stored energy is never larger than the amount of energy supplied by the environment, i.e., dissipative systems can only dissipate but not generate energy. The dissipative systems theory is closely related to the dynamic properties of a process and, in particular, to its stability properties.