Parallel Distributed Compensation for Piecewise Bilinear Models and Recurrent Fuzzy Systems Based on Piecewise Quadratic Lyapunov Functions

Piecewise Bilinear Models and Recurrent Fuzzy Systems are universal approximators for any smooth nonlinear dynamics. One of their advantage is the efficient representation of the modeled system dynamics by means of rule-bases or look-up-tables. In this paper, it is shown how to obtain provably stabilizing controllers by means of piecewise quadratic Lyapunov functions. Interpolating controllers with affine local controllers are considered for interpolation, akin to the concept of parallel distributed compensation widely used for control of Takagi-Sugeno systems.