Guaranteed Cost Control for Exponential Synchronization of Cellular Neural Networks with Mixed Time-Varying Delays via Hybrid Feedback Control

and Applied Analysis 3 The rest of this paper is organized as follows. In Section 2, we give notations, definition, propositions, and lemma for using in the proof of the main results. Delay-dependent sufficient conditions of guaranteed cost control for exponential synchronization of cellular neural networks with various activation functions and interval and distributed timevarying delays with memoryless hybrid feedback controls are presented in Section 3. Numerical examples illustrating the obtained results are given in Section 4. The paper ends with conclusions in Section 5 and cited references. 2. Preliminaries The following notation will be used in this paper:R denotes the set of all real nonnegative numbers; Rn denotes the ndimensional space and the vector norm ‖ ⋅ ‖; Mn×r denotes the space of all matrices of (n × r)-dimensions. A T denotes the transpose of matrix A; A is symmetric if A = A ; I denotes the identity matrix; λ(A) denotes the set of all eigenvalues of A; λmax(A) = max{Re λ; λ ∈ λ(A)}. x t := {x(t + s) : s ∈ [−h, 0]}, ‖x t ‖ = sup s∈[−h,0] ‖x(t + s)‖; C([0, t],Rn) denotes the set of all R-valued continuous functions on [0, t];L 2 ([0, t],R)denotes the set of all theRvalued square integrable functions on [0, t]. Matrix A is called semipositive definite (A ≥ 0) if ⟨Ax, x⟩ ≥ 0 for all x ∈ Rn; A is positive definite (A > 0) if ⟨Ax, x⟩ > 0 for all x ̸ = 0; A > Bmeans A−B > 0. The symmetric term in a matrix is denoted by ∗. In this paper, the master-slave cellular neural networks (MSCNNs) with mixed time-varying delays are described as follows: ?̇? (t) = − Ax (t) + C ̃ f (x (t)) + Dg (x (t − h 1 (t)))