On Dissipativity-Preserving for Switched Positive Takagi–Sugeno Fuzzy Delayed Systems via Switching

Abstract

In this article, we tackle the problem of analyzing dissipativity, via devising switching mechanisms, for switched positive Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. To leverage the positivity properties of state, input, and output variables, a novel concept of dissipativity is developed, focusing on linear supply rates and linear copositive storage functionals. When state information is available, the state dependent switching mechanism satisfying a dwell time constraint is introduced dependent on the constructed time-varying multiple linear copositive storage functionals. This mechanism allows for solving the dissipativity issue for the entire system without imposing any solvability requirements on subsystems and reduces the switching frequency. In cases, where state information is unavailable, dissipativity is ensured by a dwell-time dependent switching mechanism. Further, all conditions guaranteeing the solvability of the problem are presented in the form of linear vector inequalities. Two simulation examples are finally offered, demonstrating that the proposed techniques are effective and superior.