Further results on stabilization for neutral singular Markovian jump systems with mixed interval time-varying delays

Further analysis of stabilization of neutral type singular systems with mixed time‐varying delays and multiple random states

“…Consider the neutral hybrid system (5) with the following parameters: In Table 2, we can know that [28] both cases of 𝛼 = 0.1 are not feasible in Example 2, but our results are feasible. In the following, numerical simulation is carried out according to two conditions of 𝛼 = 0 or 𝛼 = 0.1.…”

“…It is worth noting that reference [18] analyzes the stability of a class of mixed delay neutral singular systems, but its neutral matrix only satisfies rank(C) > rank(E)(see Lemma 3,[18]). In addition, reference [28] analyzed the stabilization of neutral singular Markov jump systems with mixed time-varying delays, but its neutral matrix needs to satisfy rank(C) ≤ rank(E) (see Remark 1, [28]), which undoubtedly…”

“…According to (28), we perform singular value decomposition on Y 1 and Y 2 , respectively, and we can get ] .…”

“…Furthermore, in contrast, there has not been enough research on hybrid time delays in recent years [25][26][27], and much further work is needed. In [28], some scholars studied neutral singular systems with Markov jumps and mixed interval time-varying delays and provided further results for the stabilization of the system. Chen et al [25] discuss the problem of calming generalized neutral systems with neutral and state time delays, which, as concluded in the literature, does not apply to the stability of hybrid time-varying time delays.…”

An Improved Stability Criterion for Discrete-Time Linear Systems With Two Additive Time-Varying Delays

“…The main methods to reduce the conservatism include the following three aspects: a) Constructing an appropriate LKF, which contains as much information as possible about the system state variables, the time delays and some terms contained in the matrix inequality techniques. For example, a discretized LKF combined with the dwell time method [10,11], which uses the linear interpolation to discretize the LKF and divides the set matrix domains into finite points or intervals; A state decomposition LKF method [12][13][14][15][16], whcih can reduce the number of decision variables to decrease the computational complexity; The time delay product class LKFs [17][18][19][20][21]; LKFs based on Legendre polynomials and membership functions [22,23], which point that the conservatism of the conditions decreases as the order of the Legendre polynomials increases; ect.. b) Updating the inequality technique to make the upper bound of the LKF derivative tight. Such as, for discretetime systems, Bessel summation inequality [24], a novel finite sum inequality technique [25], discrete Wirtinger-based inequality technique [26,27]; for continuous systems, an inequality technique based on nonorthogonal polynomials [28,29], a generalized multiple integral inequality [30], an integral inequality based on a generalized reciprocally convex inequality [31,32], the quadratic matrix-vector form and Jensen's inequality [33], and so on.…”