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An effective approach is introduced to study the stability of continuous systems with multiple time-varying delay components. By employing a new Lyapunov–Krasovskii functional form based on delay partitioning, delay-dependent stability criteria are established for cases with or without the information of the delay rates. The contribution of the paper is 2-fold. First, it provides an improvement, as well as generalisation, of the existing stability criteria for continuous systems with multiple time-varying delay components. Second, it is illustrated numerically that the approach can be applied to estimate the delay bound for system stability in the single delay case with reduction both in conservatism and computational complexity when compared with the existing methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays. A sufficient condition, which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient, is established in terms of the linear matrix inequality (LMI) technique and a new Lyapunov-Krasovskii functional. The estimating procedure is implemented by solving a set of LMIs, which can be checked easily by effective algorithms. Under the proposed condition, the algebraic subsystems possess the same decay rate as the differential ones. Moreover, a state feedback stabilizing controller which makes the closed-loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed. Numerical examples are provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The authors deal with the problem of delay-dependent guaranteed cost control for uncertain linear systems with time-varying delays in both the state and the input. The purpose of this is to design state-feedback controllers such that the resulting closed-loop system is robustly stable, and a specified linear integral-quadratic cost function has an upper bound for all delays in the given intervals. Two types of the time-varying delays are considered. Delay-dependent sufficient conditions for the solvability of the problem are developed in terms of matrix inequalities. By the cone complementary linearisation method, desired state-feedback controllers can be constructed. A numerical example is provided to demonstrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the class of continuous-time singular linear systems with Markovian jump parameters and time delays. Sufficient conditions on the stochastic stability and stochastic stabilizability are developed. A design algorithm for a state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse free, and stochastically stable is proposed in terms of the solutions to linear matrix inequalities. [ABSTRACT FROM AUTHOR]

In the paper, the problem of H∞ filtering for a class of linear uncertain systems is studied. The parameter uncertainties are assumed to reside in a polytope. The paper is focused on the design of a parameter-dependent filter which guarantees the filtering error system to be asymptotically stable and has a prescribed H∞ performance. By employing a parameterdependent Lyapunov function approach, sufficient conditions are established for the existence of the desired filters in terms of linear matrix inequalities, which can be handled easily by using the available toolbox. Both continuous- and discrete-time cases are investigated. It is shown, via a numerical example, that the proposed filter design methods are more effective and less conservative than some existing results. [ABSTRACT FROM AUTHOR]

Simplified delay-dependent asymptotic stability conditions are provided for time-delay systems in terms of linear matrix inequalities. The redundant variables in the previous results derived by the so-called 'descriptor system approach' together with recently proposed bounding techniques are removed. Thus, the newly proposed conditions are equivalent to these obtained by the descriptor system approach but with reduced complexity. It is shown that the bounding technique does not have to be used in the derivation of our results. By the proposed method, delay- dependent results on H∞ performance analysis for time delay systems are also presented. [ABSTRACT FROM AUTHOR]

This paper deals with the fault detection problem for linear time-invariant systems with unknown disturbances. Two separate performance indices are presented to facilitate the design of desirable fault detection observers. Iterative linear matrix inequality (LMI) algorithms are proposed in order to design a fault detection observer that aims at enhancing the fault detection and attenuating the effects due to unknown inputs. Numerical examples are employed to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The output-feedback stabilisation problem is solved for discrete-time systems with time- varying delay in the state. A stability condition is first proposed, which is dependent on the minimum and maximum delay bounds. Based on this easily verifiable stability condition, the problems of stabilisation by static and dynamic output-feedback controllers are solved within the linear matrix inequality (LMI) framework. Since the obtained conditions for the existence of admissible controllers are not expressed as strict LMI conditions, the cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. In addition, the obtained results, including stability analysis, static output-feedback stabilisation and dynamic output-feedback stabilisation are further extended to discrete time-delay systems with norm- bounded uncertain parameters. Numerical examples are also presented to illustrate the applicability of the developed results. [ABSTRACT FROM AUTHOR]

An observer-based sliding mode control problem is studied for state-delayed systems with unmeasurable states and nonlinear uncertainties. The main advantage of the proposed scheme is that it eliminates the need for state variables to be fully accessible for its control. This is possible through the use of a sliding mode controller, which performs its control by employing state estimates obtained from the sliding mode observer. By means of linear matrix inequalities, a sufficient condition is then given to ensure the asymptotic stability of the overall closed-loop state-delayed system composed of the observer dynamics and the estimation error dynamics. Furthermore, it is shown that the proposed control scheme ensures the reachability of the sliding surfaces in both the state estimate space and the estimation error space. [ABSTRACT FROM AUTHOR]

The problem of sliding-mode control for a class of neutral delay systems with uncertainties in both the state matrices and the input matrix is considered. By selecting a sliding surface depending on the current state and delayed state, the paper gives a sufficient condition in terms of linear matrix inequalities (LMIs) such that the closed-loop system is guaranteed to be asymptotically stable. When LMIs are feasible, the design of the sliding surface and the slidingmode control law can be easily obtained by convex optimisation. State trajectories are attracted onto the sliding surface in a finite time and remain there for all subsequent time. A simulation illustrates the application of the method. [ABSTRACT FROM AUTHOR]

The article reports on a research based on the Robust Fault Detection (RFD) problem with the support of optimization techniques and the LMI approach. First, a necessary and sufficient condition and then a RFD problem for systems with structured uncertainties in the system matrices are planned to design RFD observers. The approaches tend to design robust fault detection observers to increase the fault detection and to attenuate the effects resulting to unknown inputs and uncertainties.