A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates
Restricted accessResearch articleFirst published online June, 2021
A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates
This work is concerned with the problem of full-order and reduced-order fault detection filters (FDFs) design in a convex optimization frame for continuous-time singular Markov jump systems (CTSMJSs) with complexity transition rates (TRs). A novel Lyapunov function construct approach is utilized to cope with the stochastic admissibility problem for CTSMJSs with complexity TRs. In order to obtain effective full-order and reduced-order FDFs, we decoupled the inequality using the presupposed Lyapunov matrix. Owing to the use of Lyapunov stochastic admissibility theory and a novel decoupling method based on convex polyhedron technique, some sufficient conditions are obtained to guarantee that the resulting full-order and reduced-order FDFs are suitable for CTSMJSs with complexity TRs. In particular, the reduced-order FDF has the advantages of small storage space and fast detection speed compared with the full order FDF. Four illustrative examples are given to explain the effectiveness of the proposed full-order and reduced-order FDFs design method.
BoukasEK (2008) Control of Singular Systems with Random Abrupt Changes. Berlin: Springer.
2.
CaoZNiuYZouY (2019) Adaptive neural sliding mode control for singular semi-Markovian jump systems against actuator attacks. IEEE Transactions on Systems, Man, and Cybernetics: Systems: 1–11.
3.
CaoZNiuYSongJ (2020) Finite-time “sliding-mode” control of Markovian jump “cyber-physical” systems against randomly occurring injection attacks. IEEE Transactions on Automatic Control65(3): 1264–1271.
4.
DaiL (1989) Singular Control Systems. New York: Springer.
5.
FengZLamJ (2013) Reliable dissipative control for singular Markov systems. Asian Journal of Control15(3): 901–910.
6.
FengZLamJ (2016) Dissipative control and filtering of discrete-time singular systems. International Journal of Systems Science47(11): 2532–2542.
7.
FengZLamJXuS, et al (2016) control with transients for singular systems. Asian Journal of Control18(3): 817–827.
8.
FengZShiP (2017a) Two equivalent sets: Application to singular systems. Automatica77(77): 198–205.
9.
FengZShiP (2017b) Sliding mode control of singular stochastic Markov jump systems. IEEE Transactions on Automatic Control62(8): 4266–4273.
10.
FengZZhengWX (2016) On reachable set estimation of delay Markov jump systems with partially known transition probabilities. Journal of the Franklin Institute353(15): 3835–3856.
11.
GaoXGaoQQiW, et al (2018) Disturbance-observer-based control for time-delay Markovian jump systems subject to actuator saturation. Transactions Institute of Measurement and Control41(3): 605–614.
12.
JiangBKaoYKarimiHR, et al (2018) Stability and stabilization for singular switching semi- Markov jump systems with generally uncertain transition rates. Transactions on Automatic Control63(11): 3919–3926.
13.
KaoYXieJWangC (2014) Stabilization of singular Markov jump systems with generally uncertain transition rates. IEEE Transactions on Automatic Control59(9): 2604–2610.
14.
KwonNKParkISParkPG, et al (2017) Dynamic output-feedback control for singular Markovian Jump system: LMI approach. IEEE Transactions on Automatic Control62(10): 5396–5400.
15.
LiBWoSZhaoJ, et al (2019) Finite-time guaranteed cost controller design for uncertain linear continuous-time singular systems. Transactions of the Institute of Measurement and Control41(12): 3507–3515.
16.
LiHShiPYaoD, et al (2016) Observer-based adaptive sliding mode control for nonlinear Markovian jump systems. Automatica64: 133–142.
17.
LiJZhaoYFengZ, et al (2019) Reachable set estimation and dissipativity for discrete-time T–S fuzzy singular systems with time-varying delays. Nonlinear Analysis: Hybrid Systems31(1): 166–179.
18.
LiLZhangQZhuB (2015) Fuzzy stochastic optimal guaranteed cost control of bio-economic singular Markovian jump systems. IEEE Transactions on Cybernetics45(11): 2512–2521.
19.
LiuGParkJHXuS., et al (2019) Robust non-fragile fault detection filter design for delayed singular Markov jump systems with linear fractional parametric uncertainties. Nonlinear Analysis Hybrid Systems 32: 65–78.
20.
MaYJiaXLiuD (2018) Finite-time dissipative control for singular discrete-Time Markov jump systems with actuator saturation and partly unknown transition rates. Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems53: 49–70.
21.
ParkISKwonNKParkPG (2019) Dynamic output-feedback control for singular Markov jump systems with partly unknown transition rates. Nonlinear Dynamics95(4): 3149–3160.
22.
ShenHMenYWuZ, et al (2019) Network-based quantized control for fuzzy singularly perturbed semi-Markov jump systems and its application. IEEE Transactions on Circuits and Systems66(3): 1130–1140.
23.
ShiYPengX (2020) Fault detection filter design of polytopic uncertain continuous-time singular Markov jump systems with time-varying delays. Complexity: 1–23.
24.
WangGZhangQYangC, et al (2015) Stabilization of singular Markovian jump systems with time-varying switchings. Information Sciences297: 254–270.
25.
WeiYParkJHQiuJ, et al (2017a) Reliable output feedback control for piecewise affine systems with Markov-type sensor failure. EEE Transactions on Circuits and Systems II: Express Briefs, 65(7): 913–917.
26.
WeiYParkJHQiuJ, et al (2017b) Sliding mode control for semi-Markovian jump systems via output feedback. Automatica81: 133–141.
27.
WeiYQiuJKarimiHR, et al (2014) Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information. Information Sciences269(10): 316–331.
28.
WeiYQiuJKarimiHR, et al (2017c) Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults, IEEE Transactions on Circuits and Systems I: Regular Papers64(1): 170–181.
29.
WuZGSuHChuJ (2011) filter design for discrete-time singular Markov jump systems with time-varying delays. Information Sciences181(24): 5534–5547.
30.
XuSLamJ (2006) Robust Control and Filtering of Singular Systems. Springer, Berlin.
31.
YaoXWuLZhengWX (2011) Fault detection filter design for Markov jump singular systems with intermittent measurements. IEEE Transactions on Signal Processing59(7): 3099–3109.
32.
YaoXZhangNJu ParkH (2020) Composite hierarchical control for Markovian jump systems with multiple disturbances and time-varying fault. Transactions Institute of Measurement and Control4(7): 1948–1956.
33.
YinYShiJLiuF, et al (2020) Robust fault detection of singular Markov jump systems with partially unknown information. Information Sciences537: 368–379.
34.
ZhangLLengYColaneriP (2016) Stability and stabilization of discrete-time semi-Markov jump linear systems via semi-Markov kernel approach. IEEE Transactions on Automatic Control61(2): 503–508.
35.
ZhangPCaoJWangG (2014) Mode-independent guaranteed cost control of singular Markov delay jump systems with switching probability rate design. International Journal of Innovative Computing, Information and Control10(4): 1291–1303.
36.
ZhangQLiLYanXG, et al (2017) Sliding mode control for singular stochastic Markov jump systems with uncertainties. Automatica, 79: 27–34.
37.
ZhangXDongJ (2020) Admissible consensus of uncertain fractional-order singular multiagent systems with actuator fault. Journal of Vibration and Control27(3–4): 264–276.
38.
ZhuangGXuSZhangB, et al (2016) Unified filters design for singular Markov jump systems with time-varying delays. Journal of the Franklin Institute. 353(15): 3739–3768.
39.
ZuoJLiuGWeiY., et al (2018) Mixed filter design for nonlinear singular Markovian jump systems with time-varying delays based on a dissipativity performance index. Transactions Institute of Measurement and Control40(9): 2779–2788.
