New bounded real lemma for discrete-time singular systems

RETRACTED: Synchronization analysis of linearly coupled singular systems

“…Singular systems are very complicated since one do not know whether the solution exists, not to mention of the stability or synchronization of the solution for the system regularity and impulse elimination. In fact, singular systems give a more general description of physical systems than the normal one, and many studies have extended concepts and results from the normal systems theory into the realm of singular systems [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. In [23], the synchronization problem of linearly coupled singular systems with the coupling matrix assumed to be symmetric and irreducible is investigated and a sufficient condition for globally asymptotic synchronization is derived based on the Lyapunov stability theory.…”

Observer-basedH∞control for uncertain singular time-delay systems with actuator saturation

“…The parametric uncertainties A, A d , B, C , and B ! are said to be admissible if both (2) and (3) hold. Now, we construct the following observer-based controller:…”

Delay-dependent robust control for discrete-time uncertain singular systems with interval time-varying delays in state and control input

“…Although this condition plays a key role in solving the H 1 control problem, it contains semi-definite and non-linear problems and is thus difficult to implement numerically. Also, Zhang et al [13] proposed a new bounded real lemma on the basis of LMI although the controller design algorithm was not given. Furthermore, Ji et al [14] developed LMI approach to the robust state feedback H 1 control for linear discrete singular systems with norm-bounded uncertainty.…”