Lyapunov Matrices for Neutral type Time Delay Systems

Instability conditions for neutral type time delay systems

“…• Using the piece-wise linear approximation or the semianalytic procedure proposed in [12], compute the Lyapunov Matrix U (τ ), τ ∈ [−h, 0] for W > 0. • Compute matrices Γ 1,2,3 by using a numerical integration method.…”

“…Equation (3) cannot be used for the construction of matrix U (τ ). In [12], a semi-analytic procedure and a piece-wise linear approximation are proposed for the computation of Lyapunov matrix U (τ ).…”

“…We first compute the Lyapunov function u(τ ) (see Fig. 1) for w = 1 using the piece-wise linear approximation procedure introduced in [12] and we obtain the values u(0) = −0.098203 and u(h) = 0.164779. Computing the values of Γ 1,2,3 with the trapezoidal rule, we get Γ 1 = Γ 2 = −0.304519 and Γ = −0.858073.…”

“…Let us select h = 7. Using the semi-analytic procedure introduced in [12] we compute the Lyapunov matrix U (τ ) for W = I (see Fig. (2)) and we obtain the values Finally Γ 1,2,3 are obtained by direct computations and we can directly check that condition (12) is satisfied hence system (16) is unstable.…”

Stability analysis and estimate of the region of attraction of a human respiratory model: [republished article]

“…Second, choosing h = 0.5 and the matrices and following the methodology proposed in (Ochoa & Kharitonov 2005, Garcia-Lozano & Kharitonov 2006 we compute the function U (τ, W ) associated to W =…”