Introduction to Time-Delay Systems by Emilia Fridman

Author:Emilia Fridman
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Example 4.8.

Consider the system

(4.154)

where is a small parameter.

We note that in this example the fast system (4.144)

is not asymptotically stable even for . (a)Consider first the non-delay systems, where . We further use LMI Toolbox of MATLAB to verify the feasibility of the strict LMIs of Proposition 4.14 for the exponential stability of (4.154). Given , by solving the strict LMIs (4.147) and with defined by (4.150), where R d  = 0, we find that the system (4.154) is exponentially stable with a decay rate δ = 0. 484. We note that the matrix in this example has eigenvalues with real parts − 0. 4845. For , the strict LMI Γ 0 < 0 is not feasible since the fast system is not asymptotically stable. Next, verifying the feasibility of the strict LMIs and with the same decision variables P 2 and P 3 we find that the system is exponentially stable with a decay rate δ = 0. 43 for .

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