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The authors investigate in this study the problem of designing decentralised quantised ℋ∞ feedback control for a class of linear interconnected discrete-time systems. The system has unknown-but-bounded couplings and interval delays. The quantiser has an arbitrary form that satisfies a quadratic inequality constraint. A linear matrix inequality (LMI)-based method using a decentralised quantised output-feedback controller is designed at the subsystem level to render the closed-loop system delay dependent asymptotically stable with guaranteed γ-level. To show the generality of the authors' approach, it is established that several cases of interest are readily derived as special cases. The authors illustrate the theoretical developments by numerical simulations. [ABSTRACT FROM AUTHOR]

This study is concerned with the stability and stabilisation for systems with interval time-varying delay. First, by appropriately choosing Lyapunov functional and using Finsler's lemma, a new delay-dependent stability criteria involving the minimum and maximum delay bounds is obtained. Second, new results for delay-dependent stabilisation of systems with interval time-varying delay are provided on the basis of a linear matrix inequality (LMI) framework. Both state- and observer-based output feedback controllers are designed. Differing existing design approach of observer-based controller, a single-step approach is proposed to overcome the drawback of the two-step LMI approach often encountered in the literature, and the conditions are also delay dependent. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of observer-based output feedback control for discrete-time systems with quantised inputs. Firstly, a new necessary and sufficient condition is established to guarantee the asymptotic stability of the closed-loop system. However, the condition is presented in terms of a matrix inequality that depends on quantisation parameters varying over certain intervals. To solve this problem, a new quantisation-density-dependent necessary and sufficient condition is derived. Based on such a condition, both full- and reduced-order observer-based quantised feedback controllers are designed via a single-step approach. Finally, numerical examples are given to show the effectiveness of the author's method. [ABSTRACT FROM AUTHOR]

New ℋ∞ controller design schemes are provided for a class of discrete-time systems with uncertain non-linear perturbations. The class includes both systems with time-varying delays and systems without delay. One design scheme is generated by state-feedback and the other scheme is based on proportional-summation-difference (PSD) feedback. An appropriate Lyapunov-Krasovskii functional (LKF) is constructed and a new parametrised characterisation is established in terms of feasibility-testing of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the theoretical developments. [ABSTRACT FROM AUTHOR]

This study investigates the H∞ control problem for a class of continuous-time Markovian jump singular systems. The authors' attention is focused on the design of state and static output feedback controllers which ensure that the closed-loop system is regular, impulse-free and stochastically stable, and satisfies a prescribed H∞ performance level. To investigate the problem of H∞ performance analysis for the system under consideration, a bounded real lemma (BRL) is provided in terms of linear matrix inequality (LMI) containing equality constraints, which may not be a problem from the theoretical point of view, but may cause great big trouble in checking the conditions numerically. To solve this problem, a new version of BRL is also provided in terms of strict LMIs. Based on this, two approaches are established to solve the problem of state feedback H∞ control, and then, the problem of static output feedback H∞ control is solved, which can also be used for solving the dynamic output feedback control problems. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Robust sliding mode control is designed for a class of uncertain systems with time delay in discrete time. The uncertainties include both mismatched parametric uncertainties in the state model and the matched external disturbance. After deriving sufficient conditions for the existence of linear sliding surfaces based on linear matrix inequality (LMI), robust reaching motion control is presented. A simulation study shows the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This study is concerned with the generalised ℋ2 and the ℋ∞ static control problems for discrete-time fuzzy systems with time-varying norm-bounded parametric uncertainties. Based on the solutions to certain linear matrix inequalities LMIs, static output feedback controllers are designed, which can ensure the asymptotic stability and the generalised ℋ2 and ℋ∞ performance level, respectively. Differenting from the existing results, the design conditions in this study are derived in terms of LMIs directly, and the local output matrices are allowed to be different. Three illustrative examples are provided to demonstrate the effectiveness and the reduced conservatism of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper deals with the class of linear discrete-time systems with random abrupt changes also known as class of Markovian jump singular systems. The problems of stochastic stability and the stochastic stabilisation (using state-feedback control and static output feedback control) are tackled. Conditions in the LMI setting to design the appropriate gains of the controllers are developed. It is shown that all the addressed problems can be solved if the corresponding developed linear matrix inequalities (LMIs) are feasible. Numerical examples are employed to show the usefulness of the proposed results. [ABSTRACT FROM AUTHOR]

The problem of robust state feedback control using delta operator approach for a class of linear fractional uncertain systems with time-varying delays is investigated. Based on Lyapunov–Krasovskii functional in delta domain, a new delay-dependent state feedback controller is presented in terms of linear matrix inequalities. The sampling-period T is an explicit parameter, and thus it is easy to observe and analyse the effect of the state feedback controller with different sampling periods. The proposed method can unify some previous related continuous and discrete systems into the framework of delta operator systems. Numerical examples are given to illustrate the effectiveness of the developed techniques. [ABSTRACT FROM AUTHOR]