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This paper considers the problems of stability, stabilization and H∞ control via memoryless state feedback for uncertain discrete-time Markovian jump linear systems with mode-dependent time delays. Based on linear matrix inequalities, delay-dependent solutions are obtained by using a descriptor model transformation of the system and by applying a new bounding technique for cross terms. Numerical examples are presented to illustrate the usefulness of the theoretical results. [Copyright &y& Elsevier]

This paper deals with the problem of delay-dependent robust stability for systems with time-varying structured uncertainties and time-varying delays. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz–Newton formula into account. Since free weighting matrices are used to express this relationship and since appropriate ones are selected by means of linear matrix inequalities, the new criteria are less conservative than existing ones. Numerical examples suggest that the proposed criteria are effective and are an improvement over previous ones. [Copyright &y& Elsevier]

This paper considers the problem of output-feedback guaranteed cost controller design for uncertain time-delay systems. By representing the time-delay system in the descriptor form and using a recent result on bounding of cross products of vectors, we obtain new delay-dependent sufficient conditions for the existence of the guaranteed cost output-feedback controller in terms of matrix inequalities. A numerical algorithm is proposed to construct a full order output feedback controller achieving a suboptimal guaranteed cost such that the system can be stabilized for all admissible uncertainties. An example is presented which shows that the proposed method can produce a lower guaranteed cost than the delay-independent method. [Copyright &y& Elsevier]

In this Letter, a thorough analysis of existence, uniqueness and globally exponential stability of the equilibrium point of neural networks with variable delays is presented. By applying M-matrix theory and some new analysis techniques, a new delay-dependent sufficient condition for global exponential stability is derived. The criteria obtained in this Letter extend and improve the existing ones, and a numerical example illustrate the effectiveness of our results. [Copyright &y& Elsevier]

This paper concerns the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. A new method based on linear matrix inequalities is presented that makes it easy to calculate both the upper stability bounds on the delays and the free weighting matrices. Since the criteria take the sizes of the neutral- and discrete-delays into account, it is less conservative than previous methods. Numerical examples illustrate both the improvement this approach provides over previous methods and the reciprocal influences between the neutral- and discrete-delays. [Copyright &y& Elsevier]

New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. [ABSTRACT FROM AUTHOR]

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach. [ABSTRACT FROM AUTHOR]

In this note, the asymptotic stability for a class of neutral systems with discrete time and distributed time delays is considered. Delay-dependent criteria are proposed to guarantee the stability for such systems. Some numerical examples are given to illustrate that our results are less conservative than previous results. [ABSTRACT FROM AUTHOR]

For continuous-time, linear descriptor system with state-delay a H∞-control problem is solved. Sufficient conditions for delay-dependent/delay-independent stability and L2-gain analysis are obtained in terms of linear matrix inequalities (LMIs). A bounded real lemma and state-feedback solutions are derived for systems which may contain polytopic parameter uncertainties. The filtering problem is also solved and an output-feedback controller is then found by solving two LMIs. The first LMI is associated with a proportional-derivative state-feedback control. The second LMI is derived in two different forms, the first one corresponds to the adjoint of the system that describes the estimation error and the other stems from the original system. These two forms lead to different results. Numerical examples are given which illustrate the effectiveness of the new theory. [Copyright &y& Elsevier]