Passive-based Analysis and Control of Takagi-Sugeno Fuzzy Systems

In this paper, sufficient LMI-based conditions for general Quadratic Supply Rate (QSR) functions, known as QSR-dissipativity of nonlinear systems in Takagi- Sugeno form are proposed. To determine the stability of negative feedback loops of two systems, it is sufficient to prove the passivity of each individual system. This property can be used to ensure the stability of even globally distributed systems if the individual local systems are passive. This is particularly relevant for the stabilization of massively distributed power systems, for example. The passivity can either be a property of non-regulated systems or non-passive systems becomes passive through feedback controller. Both cases are analyzed for the class of Takagi-Sugeno fuzzy systems.