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Absolutely exponential stability of Lur’e distributed parameter control systems. (English) Zbl 1241.93042

Summary: In this work, absolutely exponential stability of Lur’e distributed parameter control systems with delayed state has been addressed. Delay-dependent sufficient conditions for the absolutely exponential stability in Hilbert spaces are established in terms of Linear Operator Inequalities (LOIs). Finally, the wave equation is given to illustrate our result.

MSC:

93D20 Asymptotic stability in control theory
93C20 Control/observation systems governed by partial differential equations
35L05 Wave equation
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References:

[1] Lur’e, A. I.; Postnikov, V. N., On the theory of stability of control systems, Prikladnaya Matematika Mehkhanika, 8, 246-248 (1944) · Zbl 0061.19407
[2] Cao, J.; Zhong, S., New delay-dependent condition for absolute stability of Lur’e control systems with multiple time-delays and nonlinearities, Appl. Math. Comput., 194, 250-258 (2007) · Zbl 1193.93143
[3] Han, Q. L., Robust absolute stability criteria for uncertain Lur’e systems of neutral type, International Journal of Robust and Nonlinear Control, 18, 278-295 (2008) · Zbl 1284.93178
[4] Nam, P. T.; Pathirana, P. N., Improvement on delay dependent absolute stability of Lur’e control systems with multiple time delays, Appl. Math. Comput., 216, 1024-1027 (2010) · Zbl 1217.93151
[5] Fridman, E.; Orlov, Y., Exponential stability of linear distributed parameter systems with time-varying delays, Automatica, 45, 194-201 (2009) · Zbl 1154.93404
[6] Khalil, H. K., Nonlinear Systems (1996), Prentice Hall: Prentice Hall Upper Saddle River, NJ · Zbl 0626.34052
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