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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:
93D20Asymptotic stability of control systems
93C20Control systems governed by PDE
35L05Wave equation (hyperbolic PDE)
References:
[1]Lur’e, A. I.; Postnikov, V. N.: On the theory of stability of control systems, Prikladnaya matematika mehkhanika 8, 246-248 (1944)
[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 · doi:10.1016/j.amc.2007.04.034
[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)
[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 · doi:10.1016/j.amc.2010.01.090
[5]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
[6]Khalil, H. K.: Nonlinear systems, (1996)