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Absolute mean square exponential stability of Lur’e stochastic distributed parameter control systems. (English) Zbl 1242.93134

Summary: In this work, the absolute mean square exponential stability of Lur’e stochastic distributed parameter control systems has been addressed. Delay-dependent sufficient conditions for the stochastic stability in Hilbert spaces are established in terms of Linear Operator Inequalities (LOIs). Finally, the stochastic wave equation illustrates our result.

MSC:

93E15 Stochastic stability in control theory
93C25 Control/observation systems in abstract spaces
93C20 Control/observation systems governed by partial differential equations
35L05 Wave equation
93B28 Operator-theoretic methods
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References:

[1] Lur’e, A. I.; Postnikov, V. N., On the theory of stability of control systems, Prikladnaya Matematika i Mekhanika, 8, 246-248 (1944) · Zbl 0061.19407
[2] 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
[3] Han, Q. L., A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems, Automatica, 44, 272-277 (2008) · Zbl 1138.93039
[4] Fridman, E.; Orlov, Y., Exponential stability of linear distributed parameter systems with time-varying delays, Automatica, 45, 194-201 (2009) · Zbl 1154.93404
[5] Kushner, H. J., Stochastic Stability and Control (1967), Academic: Academic New York · Zbl 0178.20003
[6] Khalil, H. K., Nonlinear Systems (1996), Prentice Hall: Prentice Hall Upper Saddle River, NJ · Zbl 0626.34052
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