Controller and Filter Syntheses for Positive Takagi–Sugeno Fuzzy Systems Under $\ell _{1}$ Performance

Abstract

In this chapter, the $\ell _{1}$-induced controller and filter design problems for positive Takagi–Sugeno (T–S) fuzzy systems are investigated with the use of linear Lyapunov function. A novel performance characterization is first established to guarantee the asymptotic stability of the positive fuzzy system with $\ell _{1}$-induced performance. Then, sufficient conditions are presented to design a desired controller and an iterative convex optimization approach is developed to solve the conditions. Moreover, to estimate the output of positive T–S fuzzy systems, error-bounding positive filters are constructed. Sufficient conditions expressed by linear programming problems are derived to design the desired filters. Finally, some numerical examples are presented to show the effectiveness of the derived theoretical results.