Observer-Based Control for Piecewise-Affine Systems With Both Input and Output Quantization

Observer‐based actuator fault estimation and proportional derivative fault tolerant control for continuous‐time singular systems

“…In what follows, we aim to prove that the error system (15) satisfies the H ∞ performance index . Considering (17), under the zero initial condition, one has…”

“…Theorem 2. Given a scalar > 0, the error system (15) is asymptotically stable and satisfies the H ∞ performance (17), if there exist matrices  1 ,  2 ,  1 ,  2 as well as  > 0, such that the LMI (24) is feasible…”

“…In the work of Ning et al, based on the semi‐Markov kernel approach, the issue on observer‐based stabilization was solved effectively for nonhomogeneous semi‐Markov jump systems with mode‐switching delays. For more results, we refer to the works of Zhang et al, Li et al, Liu et al, and Lan et al…”

“…In the work of Ning et al, 16 based on the semi-Markov kernel approach, the issue on observer-based stabilization was solved effectively for nonhomogeneous semi-Markov jump systems with mode-switching delays. For more results, we refer to the works of Zhang et al, 17 Li et al, 18 Liu et al, 19 and Lan et al 20 On another research forefront, singular systems (descriptor systems or differential-algebraic systems) have a tighter representation than the traditional state-space model due to their markedly abilities in modeling many practical systems, such as mechanical systems, biological systems, and electrical networks. 21 The reason lies in the fact that, for a real plant, it always has static and dynamic constraints.…”

Disturbance‐observer–based control for Markov jump systems with time‐varying delay

“…It is well known that the disturbances usually exist in practical control processes and lead to degradation of dynamic system performance. Therefore, to ensure the stability and pursue performances, it is noted that how to reject the disturbances has become a heated topic because of its importance in both theoretical and practical applications . To solve the disturbance rejection problem, several elegant methods have been proposed, including disturbance‐observer–based control (DOBC), regulation theory, and so on.…”