Meng LI(李猛), Hui-ying SUN(孙慧影), Min SANG(桑敏)
College of Information and Electrical Engineering, Shandong Unive rsity of Science and Technology, Qingdao 266510, China
Abstract-This paper mainly discusses stabilizatbility, exact observability and exact detectability of discrete stochastic systems with both static and control dependent noise via the spectrum technique. The authors put forward a definition of the spectrum and give some theorems based on the spectru m. Then the relation between discrete generalized Lyapunov equation and discrete generalized algebraic Riccati equation is also analyzed.
Key words-spectrum technique; discrete stochastic syste ms; detectability; observability
Manuscript Number: 1674-8042(2010)04-0387-04
dio: 10.3969/j.issn.1674-8042.2010.04.19
References
[1]J.L.Willems, J.C.Willems, 1976. Feedback stabi-lizability for stoch astic systems with state and control dependent noise. Automatic, 12(3): 277-283.
[2]A.E.Bashirov, K.R.Kerimov, 1997. On controllab-ility conception f or stochastic systems. SIAM Journal on Control and Optimization, 35(2): 384-398.
[3]R.Z.Has′minskii, 1980. Stochastic Stability of Differential Equatio ns. Sijtjoff and Noordhoff, Alphen.
[4]W.L.De Koning, 1983. Detectability of linear discrete-time systems with stochastic parameters. International Journal of Control, 38(6): 1035-1046.
[5]T.Damn, 2007. On detectability of stochastic systems. Aut omatic, 43(3): 928-933.
[6]Z.Y.Li, Y.Wang, B.Zhou, et al, 2009. Detectability and observability of discrete-time stochastic systems and their applications.Automatic , 45(3): 1340-1346.
[7]W.H.Zhang, H.S.Zhang, B.S.Chen, 2008. Gener-alized lyapunov equat ion approach to state-dependent stochastic stabilization/detectability criterio n. IEEE Transactions on Automatic Control, 53(4): 1630-1642.
[8]B.S.Chen, W.H.Zhang, 2004. Stochastic control with state-dependent noise. IEEE Transactions on Automatic Control, 49(1): 45-57 .
[9]Y.Z.Liu, 1999. Backward stochastic differential equation and stochas tic systems control systems. Ph.D. Thesis, Shandong University, Jinan.
[10]W.H.Zhang, B.S. Chen, 2004. On stabilizability and exact observa bility of stochastic systems with their applications. Automatic, 40(1): 87-94.
[11]Y.L.Huang, W.H.Zhang, H.S.Zhang, 2008. Infi-nite horizon linear quadratic optimal control for discrete-time stochastic systems. Asian Journal of Control, 10(5): 608-615.
[12]M.D.Fragoso, O.L.V.Costa, C.E.de Souza, 1998. A new approach to linearly perturbed Riccati equations arising in stochastic control. Ap plied Mathematics and Optimization, 37(4): 99-126.
[13]R.Nikoukhah, B.C.Levy, A.S.Willsky, 1989. Stabi-lity, stochastic stationarity, and generalized lyapunov equations for two-point boundary-value descriptor systems. IEEE Transactions on Automatic Control, 3 4(6): 1141-1152.
[14]M.A.Rami, X.Chen, X.Y.Zhou, 2002. Discrete-time indefinite LQ cont rol with state and control dependent noise. Journal of Global Optim ization, 23(4): 245-265.
[15]J.J.Qi, W.H.Zhang, 2009. Discrete-time indefinite stochastic LQ optimal control: Infinite horizon case. Acta Automatica Sinica, 35(3): 613-617.
[16]M.Ait Rami, Xun-yu Zhou, J.B.Moore, 2000. Well-posedness and at tainability of indefinite stochastic linear quadratic control in infinite time h orizon. Systems & Control Letters, 41(5): 123-133.
[full text view]