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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:
93E15Stochastic stability
93C25Control systems in abstract spaces
93C20Control systems governed by PDE
35L05Wave equation (hyperbolic PDE)
93B28Operator-theoretic methods in systems theory
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)
[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)