Stabilisation of mode-dependent singular Markovian jump systems with generally uncertain transition rates

An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

“…The above two kind of models are maybe too restrictive in many practical situations. Therefore, a new description for the uncertain TRs is discussed [20,21]. This new model is named as general uncertain TRs (GUTRs).…”

“…Unfortunately, in practice, precise values of the TRs are difficult or even impossible to obtain due to the cost and other factors. Therefore, the analysis and synthesis method for MJS with incomplete TRs have become a research focus [12][13][14][15][16][17][18][19][20][21][22]. There are three types of descriptions for the incomplete TRs.…”

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

“…In fact, π ii may not always known, for the case of i ∈ I i uk , we can refer to [10] for the detailed proof. (2) If I i uk = ∅ , then 1 + χ i = 1 , LMI (8) will becomes a condition to check the mean-square exponential stability of the system (3) with completely known TRs.…”

“…[2][3][4][5][6][7][8] . 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] .…”

Observer-Based $$H_\infty $$ H ∞ Sliding Mode Controller Design for Uncertain Stochastic Singular Time-Delay Systems

“…Liu [13] solved the exponential robust stability and stabilization problems for uncertain time-varying delay singular systems. Kao et al [8] have recently considered stabilization of singular Markovian jump systems with generally uncertain transition rates. Sliding mode control (SMC), due to its attractive features such as fast response and good transient response, insensitivity to variations in system parameters and external disturbances, has become an effective robust control approach for a wide variety of practical engineering systems such as robot manipulators, aircraft, underwater vehicles, spacecraft, flexible space structures, electrical motors, power systems and automotive engines [3,20,32].…”