Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay

Integrated fault estimation and fault‐tolerant control for uncertain time‐varying delay nonlinear Markovian jump systems

“…It can be seen from (20) that, ifΩ i < 0, then J 1 < 0, for any (t) ≠ 0. By the Schur complement, inequalitŷ Ω i < 0 is equivalent to condition (13). Therefore, the close-loop system (12) is asymptotically stable with disturbance attenuation .…”

“…Example Consider a single‐link robot arm model cited from the works of Wang et al and Wu and Cai, and the dynamic equation is described by where p ( t ), u ( t ), and w ( t ) are the angle position of the arm, control input, and the external disturbance, respectively. Parameters , and D are the mass of payload, the acceleration of gravity, the length of the arm, the moment of inertia, and the uncertain coefficient of viscous friction, respectively.…”

“…In many cases, it is impossible or high cost to obtain the transition probability exactly. The researches on MJSs with partly unknown transition probabilities were addressed in the works of Yao et al and Sun et al Recently, the work of Wang et al considered the problem of finite‐time stability and stabilization for time‐varying delays MJSs with uncertain transition rate.…”

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

“…For example, in Wu et al, 10 the problem of delay-dependent exponential stability for uncertain singular Markovian jump systems was addressed. In Wang et al, 13 the robust H ∞ descriptor observer was proposed to tackle the simultaneous state and disturbance estimation for uncertain stochastic system. In addition, the authors considered the delay-dependent exponential stability for Markovian jump systems with time-varying delay.…”

“…By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), some sufficient criteria are derived to guarantee that the controlled singular hybrid systems with Markovian jump is robustly exponentially mean-square admissibility and has H ∞ performance . Compared with the existing works, 2,10,13,22,25,37 the main feature of our work is that the designed event-triggered sampling scheme can be suitable for the gain matrices to achieve the desired H ∞ robust performance by the use of the Matlab LMIs Toolbox. Furthermore, the developed analysis framework is more applicable for convergence analysis of robust H ∞ control of singular uncertain Markovian jump systems, and a typical example of RLC circuit is finally given to show the effectiveness of the proposed algorithms.…”