A sliding mode approach to robust stabilisation of Markovian jump linear time-delay systems with generally incomplete transition rates

Stabilization of Discrete-Time Markovian Jump Systems by a Partially Mode-Unmatched Fault-Tolerant Controller

“…On the other hand, some references [5,6,17,26] have considered other general cases that the transition rate matrix referred to continuous-time case is partially unknown, uncertain or depends on the random sojourn time. Even in reference [20], the partially accessible mode information is also referred to transition rate matrix partially unknown.…”

“…It also has been widely studied in the field of industrial process control, space flight, medical treatment, electric power and economy. During the past few decades, many important results based on kinds of systems have emerged, such as stability analysis [1][2][3][4][5][6], stabilization [7][8][9][10], delay case [11][12][13], output control [14,15], H ∞ control [16][17][18][19] and filtering [20][21][22], robust control [23][24][25], sliding control [26], state estimation [27], fault detection [28], synchronization [29,30], and so on.…”

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

“…Besides the uncertainty, time‐delay is also another common phenomena for poor performance and instability of many dynamical systems such as flight control systems, telecommunication systems, mechanical systems, and chemical engineering systems. Therefore, during the past few decades, much research efforts have been made to investigate stability criteria for various types of time‐delay systems . In general, stability analysis of time‐delay systems is classified into two categories such as delay‐independent and delay‐dependent stability criterion in which the later one uses the information of maximal delay bound and the former one does not.…”

Sliding mode control of Markovian jump systems with incomplete information on time-varying delays and transition rates

“…Recently, an interest in the uncertainty of TRs in the jumping process evoked due to the possibility of getting full information on TRs and high expense, many research activities have been attracted, such as in [9] , sufficient conditions for stochastic stability and stabilization of Markovian jump linear systems with partly unknown TRs via LMIs formulation is developed; in [10] , the authors studied the stabilization of modedependent singular MJSs with generally uncertain TRs, etc., see, e.g. [11][12][13][14][15] . While the field is not fully investigated yet, so it is significant to further study MJSs with incomplete TRs.…”

“…Such as in [19] , fuzzy logic systems-based integral sliding mode fault-tolerant control for a class of uncertain non-linear systems is investigated; and SMC design for linear systems subject to quantization parameter mismatch is studied in [20] ; including robust H ∞ control for neutral-type systems via sliding mode observer [21] . On the other hand, SMC of MJSs is also an active field, like the author considered robust stabilization of Markov jump linear time-delay systems with generally incomplete TRs in [11] . However, the state information may not always be available in practice.…”