Synthesis and stability analysis of linguistic fuzzy controlled systems

With the help of conventional linear control theory, the synthesis of linguistic fuzzy-logic controllers (FLCs) can be readily realised by employing a linear-to-fuzzy conversion algorithm which converts linear control laws into corresponding linear linguistic FLCs. The operating ranges (universes of discourse), number of linguistic labels of the antecedents and consequent, and the associated fuzzy rules can be determined systematically. With application of suitable heuristics, the developed linear linguistic FLCs become nonlinear linguistic FLCs with better performance. A novel equivalent transformation (ET) algorithm is proposed to transform the nonlinear linguistic FLC into another form which is more amenable to stability analysis. The input-output (conicity stability criterion) and state-space (multivariable circle and quadratic stability criteria) approaches are employed to study the stability analysis of a fuzzy controlled double-integrator problem