Robust stability of Fuzzy Elman Neural Network

Global Uniform Asymptotic Stability of a Class of Switched Linear Systems with an Infinite Number of Subsystems

“…It was shown that the nonlinear switched delay system is attractive and obtained the attractive region. The authors of the paper proposed three methods for existence of a common quadratic Lyapunov function for robust stability analysis of fuzzy Elman neural network [16].…”

“…The discrete time switching linear system (6) with an infinite number of switching systems of the form (16) isGUAS under arbitrary switching if there exist two numbers and such that, ‖ ‖ ≤ < 1, ‖ ‖ ≤ < 1, and ≤ < ∞ is bounded. Because of (⋅) ≤ ‖ ⋅ ‖, the discrete time switching linear system (6) with an infinite number of switching systems with the form(16) is GUAS under arbitrary switching if ( ) < 1, ( ) < 1.Example 11. Consider switching linear system (6) with two subsystems of the form(16) and let Σ be a set of triangular block matrices with blocks on the diagonal:Σ = {Σ 1 , Σ 2 } ={ shows the simulation result of Example 11.Example 12.…”

“…Because of (⋅) ≤ ‖ ⋅ ‖, the discrete time switching linear system (6) with an infinite number of switching systems with the form(16) is GUAS under arbitrary switching if ( ) < 1, ( ) < 1.Example 11. Consider switching linear system (6) with two subsystems of the form(16) and let Σ be a set of triangular block matrices with blocks on the diagonal:Σ = {Σ 1 , Σ 2 } ={ shows the simulation result of Example 11.Example 12. Consider a discrete time switching linear system of the form (16) that Σ = {Σ 1 , Σ 2 , .…”