A Lattice Control Model of Fuzzy Dynamical Systems in State-Space
Petros A. Maragos, Giorgos B. Stamou, Spyros G. Tzafestaş · Kluwer Academic Publishers eBooks · 2005
Lattice control can unify nonlinear control systems where the basic vector and signal superpositions or transformations are based on the lattice supremum and infimum. In this paper we introduce a special case of lattice control that can model fuzzy dynamical systems in state space. Vector and signal transformations are represented as lattice dilations or erosions. The state and output responses are computed via supremal convolutions based on fuzzy norms. Causality and stability issues are studied. Finally, solutions to the controllability and observability problem are found using lattice adjunctions.