In this paper, the design problem of unknown input observer for a class of nonlinear discrete time Markov jump systems has been studied. The state equation of the system with unknown input and actuator faults is considered. The unknown input observer has a relatively novel structure and can be applied to nonlinear discrete time Markov jump systems to estimate the system state and fault at the same time. Second, the design feasibility conditions of the unknown input observer based on Lyapunov function are given. Furthermore, the conditions are transformed into a set of linear matrix inequality conditions, which can be used to solve the parameters easily by using the related software toolbox. Finally, an example of nonlinear tunneling diode circuit is given to verify the feasibility and effectiveness of the proposed method.
BabaeiBShafieeM (2019) Analysis and behavior control of a modified singular prey-predator model. European Journal of Control49: 107–115.
2.
GhaffariV (2021) Robust adaptive sampled-data control scheme for a class of uncertain nonlinear systems. Circuits, Systems, and Signal Processing40(5): 2282–2301.
3.
HamdiHRodriguesMMechmecheC, et al. (2012) Fault detection and isolation in linear parameter-varying descriptor systems via proportional integral observer. International Journal of Control, Automation and Systems26(3): 224–240.
4.
HuaMGBianCKChenJF, et al. (2020) Quantized H∞ filtering for continuous-time nonhomogeneous Markov jump systems. Circuits, Systems, and Signal Processing39(8): 3833–3857.
5.
JiaQXChenWZhangYC, et al. (2015) Fault reconstruction and fault-tolerant control via learning observers in Takagi–Sugeno fuzzy descriptor systems with time delays. IEEE Transactions on Industrial Electronics62(6): 3885–3895.
6.
KomachaliFPShafieeMDarouachM (2019) Design of unknown input fractional order proportional–integral observer for fractional order singular systems with application to actuator fault diagnosis. IET Control Theory & Applications13(4): 2163–2172.
7.
KongXSLiHT (2021) Time-variant feedback stabilization of constrained delayed Boolean networks under nonuniform sampled-data control. International Journal of Control, Automation, and Systems19(5): 1819–1827.
8.
LiHDHanCYZhangHS (2018) Optimal control problem for discrete-time Markov jump systems with indefinite weight costs. In: International conference on intelligent robotics and applications, Newcastle, NSW, Australia, 9–11 August, pp. 144–152. Cham: Springer.
9.
LiJHZhangQLYanXG, et al. (2017) Integral sliding mode control for Markovian jump T-S fuzzy descriptor systems based on the super-twisting algorithm. IET Control Theory & Applications11(8): 1134–1143.
10.
LinWSLiXMYaoDY, et al. (2019) Observer-based event-triggered sliding mode control for Markov jump systems with partially unknown transition probabilities. International Journal of Control, Automation and Systems17(7): 1626–1633.
11.
LongYParkJHYeD (2019) Finite frequency fault detection for a class of nonhomogeneous Markov jump systems with nonlinearities and sensor failures. Nonlinear Dynamics96(1): 285–299.
12.
MaXJSunZQHeYY (1998) Analysis and design of fuzzy controller and fuzzy observer. IEEE Transactions on Fuzzy Systems6(1): 41–51.
13.
MuYFZhangHGSuHG (2020) Unknown input observer synthesis for discrete-time T-S fuzzy singular systems with application to actuator fault estimation. Nonlinear Dynamics100(4): 3399–3412.
14.
PanSYYeZYZhouJ (2020) Fault detection filtering for a class of nonhomogeneous Markov jump systems with random sensor saturations. International Journal of Control, Automation and Systems18(2): 439–449.
15.
RodriguesMHamdiHTheilliolD, et al. (2015) Actuator fault estimation based adaptive polytopic observer for a class of LPV descriptor systems. International Journal of Robust and Nonlinear Control25(5): 673–688.
16.
SakthivelRSuveethaVTDivyaH, et al. (2020) Fault detection finite-time filter design for T–S fuzzy Markovian jump system with missing measurements. Circuits, Systems, and Signal Processing40(4): 1607–1634.
17.
ShangHQiWHZongGD (2020) Asynchronous H-infinity control for positive discrete-time Markovian jump systems. International Journal of Control, Automation and Systems18(2): 431–438.
18.
ShenMQZhangHNParkJH (2018) Observer-based quantized sliding mode H∞ control of Markov jump systems. Nonlinear Dynamics92(2): 415–427.
19.
TanLHLiCDHuangJJ (2020) Neural network-based event-triggered adaptive control algorithms for uncertain nonlinear systems with actuator failures. Cognitive Computation12(6): 1370–1380.
20.
TianYTLiuWQueXJ (2020) Feedback stabilization of discrete time singularly perturbed systems with communication constraints. Asian Journal of Control22(4): 1484–1493.
21.
VuVPWangWJZuradaJM, et al. (2018) Unknown input method based observer synthesis for a discrete time uncertain T–S fuzzy system. IEEE Transactions on Fuzzy Systems26(2): 761–770.
22.
WangYQChenFZhuangGM (2020) Dynamic event-based reliable dissipative asynchronous control for stochastic Markov jump systems with general conditional probabilities. Nonlinear Dynamics101(1): 465–485.
23.
WangYYKarimiHRLamHK, et al. (2020) Fuzzy output tracking control and filtering for nonlinear discrete-time descriptor systems under unreliable communication links. IEEE Transactions on Cybernetics50(6): 2369–2379.
24.
YinKYangDDLiuJ, et al. (2020) Asynchronous control for positive Markov jump systems. International Journal of Control, Automation and Systems19: 646–654.
25.
YinYYShiPLiuF, et al. (2015) Robust filtering for nonlinear nonhomogeneous Markov jump systems by fuzzy approximation approach. IEEE Transactions on Cybernetics45(9): 1706–1716.
26.
ZerariNChemachemaM (2021) Event-triggered adaptive output-feedback neural-networks control for saturated strict-feedback nonlinear systems in the presence of external disturbance. Nonlinear Dynamics104(2): 1343–1362.
27.
ZhangJFRaissiTLiSC (2019) Non-fragile saturation control of nonlinear positive Markov jump systems with time-varying delays. Nonlinear Dynamics97(2): 1495–1513.
28.
ZhangQLXingSY (2014) Stability analysis and optimal control of stochastic singular systems. Optimization Letters8(6): 1905–1920.
29.
ZhangQLLiJHSongZY (2018) Sliding mode control for discrete-time descriptor Markovian jump systems with two Markov chains. Optimization Letters12(6): 1199–1213.
30.
ZhangXMLuGPZhengYF (2008) Observer design for descriptor Markovian jumping systems with nonlinear perturbations. Circuits, Systems, and Signal Processing27(1): 95–112.
31.
ZhangYZhaoYYXuT, et al. (2016) Pth moment absolute exponential stability of stochastic control system with Markovian switching. Journal of Industrial and Management Optimization12(2): 471–486.
32.
ZhangYJOuYS (2018) Resilient dissipative filtering for uncertain Markov jump nonlinear systems with time-varying delays. Circuits, Systems, and Signal Processing37(2): 636–657.
