Abstract
New analysis and control design conditions of discrete‐time fuzzy systems are proposed. Using fuzzy Lyapunov′s functions and introducing slack variables, less conservative conditions are obtained. The controller guarantees system stabilization and ℋ∞ performance. Numerical tests and a practical experiment in Chua′s circuit are presented to show the effectiveness.
Highlights
Model-based fuzzy control is a widespread approach to deal with complex nonlinear dynamics 1
Takagi-Sugeno TS fuzzy model 2 is a landmark. It consists on fuzzy rules describing global semiglobal dynamics as linear models locally valid interpolated by membership functions
This paper presents new sufficient conditions to H∞ control for DFS in the TS form
Summary
Model-based fuzzy control is a widespread approach to deal with complex nonlinear dynamics 1. Methodologies based on Lyapunov’s functions provide a straightforward way to describe stability and control design issues of TS systems by means of linear matrix inequalities LMIs 6 , of which the solutions can be computed in polynomial-time by convex optimization techniques. Most efforts deal with sufficient conditions for the existence of a CQLF 3 , a single quadratic function that guarantee stability for all fuzzy subsystems. 15 provides a successful approach to introduce slack matrix variables into the stabilization control, enhancing the numerical behavior of LMI solvers. This strategy was further extended to H∞ control in 11 and is used in this paper. Transpose of vectors and matrices are indicated by the superscript ; the symbol denotes transposed terms in symmetric matrices; the sets {1, 2, . . . , r} and {1, 2, . . . , s} are indicated by R and S, respectively; l2 is the discrete Lebesgue space; · 2 is the l2 norm
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