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Dynamics of milling process is governed by a set of delay differential equations with periodic coefficients.
Secondly, the interconnection of the system, shaper and the controller is formulated as a set of delay differential algebraic equations.
By implementing linear matrix inequality optimization approach together with delay fractioning technique, a new set of delay dependent sufficient condition is derived which guarantees that the uncertain singular system to be regular, impulse-free and stochastically stable.
We observe that with finer quantization of slot sizes, the distribution interval of the last node has not only a smaller maximum delay but also a smaller possible set of delay values that can be expected.
By implementing an appropriate Lyapunov Krasovskii functional together with Wirtinger-based inequality, a new set of delay dependent sufficient condition is derived in terms of linear matrix inequalities which guarantees that the singular Markovian jump system is regular, impulse-free and stochastically stable.
By applying the inequality pap−1b⩽(p−1)ap+bp, where p denotes a positive integer and a,b denote nonnegative real numbers, and constructing an appropriate form of Lyapunov functionals we obtain a set of delay independent and easily verifiable sufficient conditions under which the network has a unique equilibrium which is globally exponentially stable.
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At the first step, a short time delay was artificially introduced into the control loop and the dynamic equations of the aeroelastic system with delayed control were converted into a set of delay-free state-space equations by using a state transformation.
The model comprises a set of delay-differential equations; thus, the phase-space of the system has an infinite dimension.
Then a set of delay-dependent sufficient conditions for the existence of desired robust H∞ filters is expressed in terms of linear matrix inequalities.
Based on the Lyapunov stability theory, a new set of delay-dependent conditions is obtained in terms of linear matrix inequalities to determine the system stability and achieve the sampled-data PI control design.
By employing Lyapunov technique together with Wirtinger based integral inequalities, a new set of delay-dependent sufficient conditions is established which assures that the resulting closed-loop system is finite-time bounded and finite-time (Q,S,R −μ dissipative.
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Justyna Jupowicz-Kozak
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