On Controllability and Observability of Fuzzy Dynamical Matrix Lyapunov Systems

Abstract EN

We provide a way to combine matrix Lyapunov systems with fuzzy rules to form a new fuzzy system called fuzzy dynamical matrix Lyapunov system, which can be regarded as a new approach to intelligent control.

First, we study the controllability property of the fuzzy dynamical matrix Lyapunov system and provide a sufficient condition for its controllability with the use of fuzzy rule base.

The significance of our result is that given a deterministic system and a fuzzy state with rule base, we can determine the rule base for the control.

Further, we discuss the concept of observability and give a sufficient condition for the system to be observable.

The advantage of our result is that we can determine the rule base for the initial value without solving the system.