References
1. Krasovskii NM, Lidskii EA (1961) Analytical design of controllers in systems with random
attributes, automation and remote control, v22 (I. III), II, pp 1021–2025
2. Sworder DD (1969) Feedback control of a class of linear systems with jump parameters. IEEE
Trans Autom Control 14(1):9–14
3. Wonham WM (1971) Random differential equations in control theory. Probabilistic Methods
Appl Math 2:131–212
4. Ji Y, Chizeck HJ (1990) Controllability, stability and continuous-time Markovian jump linear
quadratic control. IEEE Trans Autom Control 35(7):777–788
5. Kushner H (1967) Stochastic stability and control. Academic, New York
6. Feng X, Loparo KA, Ji Y, Chizeck HJ (1992) Stochastic stability properties of jump linear
systems. IEEE Trans Autom Control 37(1):38–53
7. Boukas EK, Shi P (1998) Stochastic stability and guaranteed cost control of discrete-time
uncertain systems with Markovian jumping parameters. Int J Robust Nonlinear Control
8(13):1155–1167
8. Boukas EK, Shi P, Benjelloun K (1999) On stabilization of uncertain linear systems with
jump parameters. Int J Control 72(9):842–850
9. Boukas EK, Liu Z (2002) Deterministic and stochastic time-delay systems. Birkhauser, Boston
10. Park BG, Lee JW, Kwon WH (1997) Receding horizon control for linear discrete systems
with jump parameters. IEEE Int Conf Decis Control 4:3956–3957
11. Park BG, Kwon WH (2002) Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems. Automatica 38(1):1229–1235
12. Costa OLV, Do Val JBR, Geromel JC (1999) Continuous-time state-feedback H 2 control of
Markovian jump linear system via convex analysis. Automatica 35(2):259–268
13. Costa OLV, Marques RP (2000) Robust H 2 control for discrete-time Markovian jump linear
systems. Int J Control 73(1):11–21
14. De Farias DP, Geromel JC, Do Val J, Costa OLV (2000) Output feedback control of Markov
jump linear systems in continuous-time. IEEE Trans Autom Control 45(5):944–949
15. Mao X (1999) Stability of stochastic differential equations with Markovian switching. Stoch
Process Their Appl 79(1):45–67
16. Boukas EK (2005) Stochastic switching systems: analysis and design. Birkhauser, Basel
17. Costa OLV, Fragoso MD, Marques RP (2005) Discrete-time Markov jump linear systems.
Springer, London
18. Shi P, Xia Y, Liu GP, Rees D (2006) On designing of sliding-mode control for stochastic jump
systems. IEEE Trans Autom Control 51(1):97–103
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5
171
1. Krasovskii NM, Lidskii EA (1961) Analytical design of controllers in systems with random
attributes, automation and remote control, v22 (I. III), II, pp 1021–2025
2. Sworder DD (1969) Feedback control of a class of linear systems with jump parameters. IEEE
Trans Autom Control 14(1):9–14
3. Wonham WM (1971) Random differential equations in control theory. Probabilistic Methods
Appl Math 2:131–212
4. Ji Y, Chizeck HJ (1990) Controllability, stability and continuous-time Markovian jump linear
quadratic control. IEEE Trans Autom Control 35(7):777–788
5. Kushner H (1967) Stochastic stability and control. Academic, New York
6. Feng X, Loparo KA, Ji Y, Chizeck HJ (1992) Stochastic stability properties of jump linear
systems. IEEE Trans Autom Control 37(1):38–53
7. Boukas EK, Shi P (1998) Stochastic stability and guaranteed cost control of discrete-time
uncertain systems with Markovian jumping parameters. Int J Robust Nonlinear Control
8(13):1155–1167
8. Boukas EK, Shi P, Benjelloun K (1999) On stabilization of uncertain linear systems with
jump parameters. Int J Control 72(9):842–850
9. Boukas EK, Liu Z (2002) Deterministic and stochastic time-delay systems. Birkhauser, Boston
10. Park BG, Lee JW, Kwon WH (1997) Receding horizon control for linear discrete systems
with jump parameters. IEEE Int Conf Decis Control 4:3956–3957
11. Park BG, Kwon WH (2002) Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems. Automatica 38(1):1229–1235
12. Costa OLV, Do Val JBR, Geromel JC (1999) Continuous-time state-feedback H 2 control of
Markovian jump linear system via convex analysis. Automatica 35(2):259–268
13. Costa OLV, Marques RP (2000) Robust H 2 control for discrete-time Markovian jump linear
systems. Int J Control 73(1):11–21
14. De Farias DP, Geromel JC, Do Val J, Costa OLV (2000) Output feedback control of Markov
jump linear systems in continuous-time. IEEE Trans Autom Control 45(5):944–949
15. Mao X (1999) Stability of stochastic differential equations with Markovian switching. Stoch
Process Their Appl 79(1):45–67
16. Boukas EK (2005) Stochastic switching systems: analysis and design. Birkhauser, Basel
17. Costa OLV, Fragoso MD, Marques RP (2005) Discrete-time Markov jump linear systems.
Springer, London
18. Shi P, Xia Y, Liu GP, Rees D (2006) On designing of sliding-mode control for stochastic jump
systems. IEEE Trans Autom Control 51(1):97–103
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5
171