We study a delayed fuzzy $H_{\infty }$ control problem for an offshore platform under external wave forces. First, by considering perturbations of the masses of the platform and an active mass damper, a Takagi–Sugeno fuzzy model is established. Then, by introducing time delays into the control channel, a delayed fuzzy state feedback $H_{\infty }$ controller is designed. Simulation results show that the delayed fuzzy state feedback $H_{\infty }$ controller can reduce vibration amplitudes of the offshore platform and can save control cost significantly.

We investigate delayed state feedback control of a periodic-review inventory management system with perishable goods. The stock under consideration is replenished from multiple supply sources. By using delayed states as well as current states of the inventory system, a delayed feedback $H_{\infty }$ control strategy is developed to mitigate bullwhip effects of the system. Some conditions on the existence of the delayed feedback $H_{\infty }$ controller are derived. It is found through simulation results that the proposed delayed $H_{\infty }$ control scheme is capable of improving the performance of the inventory management significantly. In addition, the delayed controller is better than the traditional delay-free $H_{\infty }$ controller.

Singular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.

We consider feedback predictive control of a discrete nonhomogeneous Markov jump system with nonsymmetric constraints. The probability transition of the Markov chain is modelled as a time-varying polytope. An ellipsoid set is utilized to construct an invariant set in the predictive controller design. However, when the constraints are nonsymmetric, this method leads to results which are over conserved due to the geometric characteristics of the ellipsoid set. Thus, a polyhedral invariant set is applied to enlarge the initial feasible area. The results obtained are for a more general class of dynamical systems, and the feasibility region is significantly enlarged. A numerical example is presented to illustrate the advantage of the proposed method.

We derive absolute stability results of Popov-type for infinite-dimensional systems in an input-output setting. Our results apply to feedback systems where the linear part is the series interconnection of an $L^2$-stable linear system and an integrator, and the non-linearity satisfies a sector condition which allows for non-linearities with lower gain equal to zero (such as saturation, or more generally, bounded non-linearities). These results are used to prove convergence and stability properties of low-gain integral feedback control applied to $L^2$-stable linear systems subject to actuator and sensor non-linearities. The class of actuator/sensor non-linearities under consideration contains standard non-linearities which are important in control engineering such as saturation and deadzone. Moreover, we use the input-output theory developed to derive state-space results on absolute stability and low-gain integral control for strongly stable well-posed infinite-dimensional linear systems.