Observer-based finite-time control of time-delayed jump systems

Finite-timeH∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

“…It should be pointed out that finite-time stability does not imply Lyapunov stability, and Lyapunov stability does not contain finite-time stability since the transient behaviour of the system response may exceed the prescribed bound. Recently, some available results on finite-time control for Markovian switching system have been reported (He, 2010;Zhang, Liu, & Song, 2013;Zhao, Shen, Li, & Wang, 2013;Zuo, Liu, Wang, & Li, 2012).…”

Finite-timeH∞fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions

“…[9,10] Given a time constant T > 0, the Markovian jump delayed system (1) is stochasti- Lemma 2.1. [16] For any matrix X = X > 0, scalars a and b: a < b, and vector x : [a, b] → R n such that the integration concerned is well defined, then…”

“…[9,10] Given a time constant T > 0, the Markovian jump delayed system (1) is stochastically finite-time bounded with respect to (c 1 , c 2 , T, R rt , d), if there exist a matrix R rt > 0 and scalars c 1 , c 2 > 0, such that for all the disturbances ω(t) satisfying (2), condition(10) holds.…”

Finite‐time stabilisation for Markov jump systems with Gaussian transition probabilities

“…As an essential system parameter, the transition probabilities (TPs) depict the random uncertainties of the transition between possible system behaviour patterns. Under the assumption of time invariant TPs, the finite-time analysis and synthesis problems for MJSs have been investigated, see for examples [15][16][17][18] and the references therein. In practical applications, TPs are generally determined by physical experiments or numerical simulation, and only the estimated values of TPs are available.…”