Reliable sliding mode finite‐time control for discrete‐time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities

Abstract

Summary This paper focuses on the problem of finite‐time H∞ control for one family of discrete‐time uncertain singular Markovian jump systems with sensor fault and randomly occurring nonlinearities through a sliding mode approach. The failure of sensor is described as a general and practical continuous fault model. Nonlinear disturbance satisfies the Lipschitz condition and occurs in a probabilistic way. Firstly, based on the state estimator, the discrete‐time close‐loop error system can be constructed and sufficient criteria are provided to guarantee the augment system is sliding mode finite‐time boundedness and sliding mode H∞ finite‐time boundedness. The sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval, and the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities through a decoupling technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Adaptive Backstepping Sliding Mode Dynamic Positioning System for Pod Driven Unmanned Surface Vessel Based on Cerebellar Model Articulation Controller

“…In practical control, the uncertainties and disturbances are usually unknown. Therefore, it is difficult to determine the upper bound of the total uncertainties F [29]- [31]. An adaptive method can be used to estimate the total uncertainties F.…”

Fault accommodation controller under Markovian jump linear systems with asynchronous modes

“…By pre and pos multiplying (43) by diag(I, −1 i , I), and (44) by diag( −1 i , −1 i , I) we get that (9), (11), hold with the closed-loop matrices of system (17). Consequently we can rewrite (33) as…”

“…10 The use of sliding mode  ∞ finite-time boundedness in the discrete-time domain under the Markovian jump system framework has also been used for fault accommodation. 11 When Markovian jump systems with mode-dependent interval time-varying delay and Lipschitz nonlinearities is considered, an FTC approach has also been well studied. 12 For multiagent systems with a switching topology, a consensus algorithm-based FAC has been investigated for such systems.…”

“…Regarding more recent works, we can, for instance, encounter methods that use an augmented system as a descriptor system associated with a sliding mode observer for MJLS 10 . The use of sliding mode finite‐time boundedness in the discrete‐time domain under the Markovian jump system framework has also been used for fault accommodation 11 . When Markovian jump systems with mode‐dependent interval time‐varying delay and Lipschitz nonlinearities is considered, an FTC approach has also been well studied 12 .…”

$${H_\infty }$$/passive synchronization for complex dynamical networks with semi-Markovian jump and coupling time-varying delays based on sampled-data control

“…It is clear that most of stability theory investigated in general systems cannot be directly extended to the Markovian jump systems. At present, research on the Markovian jump systems has achieved many significant results, see for example (Shi and Li 2015;Liu et al 2018b;Huo et al 2017). Recently, discuss the actuator failure problem of the Markovian jump system based on the quantitative measurement of the sliding mode observer.…”