This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes and references
L. Arnold, Stochastic Differential Equations: Theory and Applications. John Wiley, New York, 1974.
L. Arnold, Random Dynamical Systems, Springer-Verlag, Berlin, 1988.
H. Bunke, Gewöhnliche Differential-gleichungen mit zufäligen Parametern, Academie Verlag, Berlin, 1972.
G. Da Prato, J. Zabczyk, Stochastic Equations in Infinite Dimension, Cambridge Univ. Press, Cambridge, UK, 1992.
V. Dragan, T. Morozan, Stability and robust stabilization to linear stochastic systems described by differential equations with Markov jumping and multiplicative white noise, Stock Analy. Appl., 20(1) (2002), 33–92.
X. Feng, K.A. Loparo, Y. Ji, H.J. Chizeck, Stochastic stability properties of jump linear systems. IEEE Trans. Automat. Control, 37(1) (1992), 38–53.
M.D. Fragoso, O.L.V. Costa, A Unified Approach for Mean Square Stability of Continuous-Time Linear Systems with Markov Jumping Parameters and Additive Disturbances. LNCC Internal Report no. 11/1999 (1999).
Y. Ji, H.J. Chizeck, Controllability, stabilizability and continuous-time Markovian jump linear quadratic control, IEEE Trans. Automat. Control, 35(7) (1990), 777–788.
I. Kats, N.N. Krasovskii, On stability of systems with random parameters (in Russian), P.M.M., 24 (1960), 809–823.
R.Z. Khasminskii, Stochastic Stability of Differential Equations. Sÿthoff and Noordhoff Alpen aan den Rijn, NL, 1980.
H. Kushner, Stochastic Stability and Control, Academic Press, New York, 1967.
G.S. Ladde, V. Lakshmikantham, Random Differential Inequalities, Academic Press, New York, 1980.
Levit, V.A. Yakubovich, Algebraic criteria for stochastic stability of linear systems with parametric excitation of white noise type, Prikl. Mat., 1 (1972), 142–147.
M. Lewin, On the boundedness measure and stability of solutions of an Itô equation perturbed by a Markov chain, Stoch. Anal. Appl., 4(4) (1986), 431–487.
K.A. Loparo, Stochastic stability of coupled linear systems: a survey of method and results. Stoch. Anal. Appl., 2 (1984), 193–228.
X. Mao, Stability of stochastic differential equations with Markov switching, Stoch. Process. Appl., 79 (1999), 45–67.
M. Mariton, Jump Linear Systems in Automatic Control, Marcel Dekker, New York and Basel, 1990.
M. Mariton, Almost sure and moments stability of Jump linear systems, Systems Control Lett., 11 (1988), 393–397.
T. Morozan, Optimal stationary control for dynamic systems with Markov perturbations, Stoch. Anal. Appl., 1(3) (1983), 299–325.
T. Morozan, Stability and control for linear systems with jump Markov perturbations. Stock. Anal. Appl., 13(1) (1995), 91–110.
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media LLC
About this chapter
Cite this chapter
(2006). Exponential Stability and Lyapunov-Type Linear Equations. In: Mathematical Methods in Robust Control of Linear Stochastic Systems. Mathematical Concepts and Methods in Science and Engineering, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-0-387-35924-3_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-35924-3_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-30523-3
Online ISBN: 978-0-387-35924-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)