Stabilization of Positive 2D Fractional-Order Continuous-Time Systems with Delays

Admissibility and robust H∞ controller design for uncertain 2D singular discrete systems with interval time‐varying delays

“…Moreover, the stabilizing feedback controller gain is given by K = Y −1 W. Remark 7. Many practical applications can be characterized by 2D singular models with time delay such as electrical circuit networks, 10,27 dynamical processes that can be modeled as partial differential equations with time delays, 11,26 such as the Darboux equations used in modeling gas absorption, water stream heating, air drying, and the thermal process in chemical reactors (see example 2), and so forth. Furthermore, an advantage of our approach is that it can be easily extended to cover other classes of systems, like 2-D switched systems 24,52 and 2-D Fuzzy systems.…”

“…The phenomena of time delays are considered here, as they are frequently encountered in many control systems such as communication, process control systems, switched control systems and networked control systems. Many researches shall therefore consider systems with delays for 1D systems (see, e.g., Zhou Gu et al; 18,19 Rajchakit; 20,21 Phat and Ratchagit; 22 Xu and Lam 23 ) and also for 2-D systems (see, e.g., Badie et al; 24,25 Xuhui et al; 26 Dami et al; 27 Van Hien and Trinh; 28 Benhayoun et al; 29 Huang and Xiang 30 ). There have been a few papers concerning the problems of stability and stabilization of 2-D singular systems, for example Zou and Campbell 31 proposed the concept of jump modes and related stability for 2-D singular systems, it must be mentioned that the presence of jump modes can reduce the cost performance index of the system, in fact we must make sure that the previous system is admissible, which means that the system is regular, jump mode free and stable.…”

Asymptotic Stability of 3D Stochastic Positive Linear Systems with Delays

“…Asymptotic stability of second and third-order stochastic differential equations has been studied using a suitable Lyapunov-Krasovskii function to investigate the 0 solution [10,11]. Dami et al [12] derived the asymptotic stability and stabilization criteria based on the Lyapunov-Krasovskii function for a class of positive fractional order of 2D linear systems with and without delays. Yang and Zheng [13] have studied and investigated the problem of sliding mode control to extend the idea of model transformation for 2D Fornasini-Marchesini local state-space model.…”

Finite-time boundedness of two-dimensional positive continuous-discrete systems in Roesser model

“…A necessary and sufficient stability criterion for positive 2-D continuous-time systems with multiple delays was proposed in Duan et al (2019). Stabilization of positive 2-D fractional-order continuous-time systems with delays was investigated in Dami et al (2019). Stability conditions for positive continuous-discrete 2-D linear systems were proposed in Kaczorek (2011).…”