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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.
93E15Stochastic stability
93C25Control systems in abstract spaces
93C20Control systems governed by PDE
35L05Wave equation (hyperbolic PDE)
93B28Operator-theoretic methods in systems theory
[1]Lur’e, A. I.; Postnikov, V. N.: On the theory of stability of control systems, Prikladnaya matematika i mekhanika 8, 246-248 (1944)
[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)
[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 · doi:10.1016/j.automatica.2007.04.009
[4]Fridman, E.; Orlov, Y.: Exponential stability of linear distributed parameter systems with time-varying delays, Automatica 45, 194-201 (2009) · Zbl 1154.93404 · doi:10.1016/j.automatica.2008.06.006
[5]Kushner, H. J.: Stochastic stability and control, (1967)
[6]Khalil, H. K.: Nonlinear systems, (1996)