Improved results for stochastic stabilization of a class of discrete-time singular Markovian jump systems with time-varying delay

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

“…Then, the SMC law is designed to make sure that the closed-loop state trajectories of the system will be driven onto the quasi-sliding surface and remain on it after that. The main contributions of this study are summarized as follows:An effective LMI-based sufficient design condition is developed to ensure that the sliding mode dynamics satisfies the H ∞ performance requirements (i.e., stochastic admissibility with a prescribed H ∞ performance) in the presence of exogenous disturbances and also partly known transition probabilities of the Markov chain.Compared with some available methods for H ∞ state feedback synthesis (see, e.g., Chadli and Darouach (2013); Long and Zhong (2017); Wang et al (2015a)), the developed LMI condition has the advantage of determining the mode-dependent parameter of the sliding surface without imposing any constraints on the introduced free matrices. Hence, it is expected to reduce the conservativeness of the obtained results over the existing ones.…”

“…2. Compared with some available methods for H ∞ state feedback synthesis (see, e.g., Chadli and Darouach (2013); Long and Zhong (2017); Wang et al (2015a)), the developed LMI condition has the advantage of determining the mode-dependent parameter of the sliding surface without imposing any constraints on the introduced free matrices. Hence, it is expected to reduce the conservativeness of the obtained results over the existing ones.…”

A new result on stability analysis for discrete system with interval time-varying delays

“…It is worth noting that not only continuous-time systems, but also discrete-time systems play an important role and have received extensive attention in the literature [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. In [12], by using the Wirtinger-based inequality an improved stability condition is obtained.…”

Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

“…Numerous publications have considered the l 2 , l 1 norm minimization problem independently in the fields of signal processing and image processing . Other methods dealing with different type of sampling data also could be found in previous studies in control theory. However, because of uncertainty of the noises, it may not work well when only l 2 or l 1 norm model is used.…”