AsynchronousH∞observer-based control synthesis of nonhomogeneous Markovian jump systems with generalized incomplete transition rates

Event-Triggered Non-PDC Filter Design of Fuzzy Markovian Jump Systems under Mismatch Phenomena

“…where G ( θ) = U (3) ( θ)G ( θ) and F ( θ) = U (3) ( θ)F ( θ). Therefore, condition (36) boils down to (26), which becomes the stochastic stability and strict (Q, S, R)-β-dissipativity condition.…”

“…(3) (θ)F (θ) and G (θ) = U (3) (θ)G (θ) as (37). Thus, the non-PDC-based PLMIs in Lemma 3 can be also relaxed according to Lemma 1, as shown in the proof of Theorem 1.…”

“…As is well known, the Markovian jump system model has the advantage that it is very suitable for characterizing dynamic hybrid systems with abrupt parameters or structural changes (see [1][2][3][4]). Furthermore, it has also been recognized that the T-S fuzzy system model has an excellent ability to represent nonlinear systems by blending local linear systems (refer to [5][6][7][8][9][10][11]).…”

Asynchronous mode‐dependent sampled‐data control of non‐homogeneous Markovian jump linear systems via an improved looped‐functional approach

“…Therefore, based on the S-procedure, the relaxed condition of (59) subject to (64) is given as (53). (ii) In the second case, using (54), we can convert ( 56) into (58) (⇔ (59)).…”

“…Proof Based on (21), there exists a sufficiently small scalar $${\lambda }> 0$$ such that $$\nabla V(t,r(t)) \le -{\lambda }||x(t)||^2_2, t \in [t_k, t_{k+1})$$. Then, according to the means of generalised Dynkin's formula [53], it is given that $$\begin{eqnarray} V(t_{k+1},r(t_{k+1})) - V(t_k,r(t_k)) \le - {\lambda }\int _{t_k}^{t_{k+1}} {|| x(t) ||}_2^2dt.\quad \end{eqnarray}$$Furthermore, since it follows from (22) that …”