A strictly bounded real lemma for singular Markovian jump systems

Fault estimate and fault‐tolerant control for hybrid systems based on the extended state method

“…Theorem 1 (Stability analysis). For 𝛾 > 0, the stochastic stability of systems (22) and (23) with 𝜔 k = 0 is analyzed and ( 24) is satisfied if there exist  T i =  i > 0 such that (25) holds.…”

“…Consider systems ( 1)-( 3) with observer ( 14)-( 18) and controller (20). For 𝛾 > 0, the stochastic stability of systems (22) and (23) with 𝜔 k = 0 is analyzed and ( 24) holds, if there exist…”

“…1. For all i = 1, … , N, 𝜔 k = 0, that is, 𝜔 k = 0, systems (22) and ( 23) is stochastically stable. 2.…”

“…This kind of systems is widely used when sudden failures or environmental changes happen, such as power systems, aerospace systems, network control systems. In the decades, Markov jump systems have received a lot of attention from many scholars, for example, the problems of Markov jump systems on robust control analysis, [21][22][23] admissibility analysis, 24 and filter 25,26 have been well solved.…”

Improved passivity‐based control for Markovian jump singular systems with aperiodic sampling and actuator failures

“…Especially, Markovian jump singular systems (MJSSs) describing singular systems with random changes in parameters or structure have been extensively researched. In addition, related studies for MJSSs are reported, 20‐22 for instance, robust stabilization, 23 stochastic admissibility and stability analysis, 24,25 H‐infinity filtering, 26,27 sliding mode control, 28‐30 and the references therein. However, the above studies are mainly for MJSSs with fully known TRs.…”