Delay-dependent State Research Articles

Robust mode delay-dependent ℋ ∞ control of discrete-time systems with random communication delays

This study considers stability and robust mode delay-dependent ℋ∞ controller design for discrete-time systems with random communication delays. Communication delays between sensors and controllers are modelled by a finite state Markov process. Based on Lyapunov–Krasovskii functional, a novel methodology for designing a mode delay-dependent state feedback controller has been proposed. The authors also show that the existing delay-dependent approach is a special case of the mode delay-dependent approach proposed in this study. The mode delay-dependent controller is obtained by solving linear matrix inequality optimisation problems using the cone complementarity linearisation algorithm. The effectiveness of the proposed design methodology is verified by a numerical example.

Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks

This paper proposes a new delay-dependent state estimator for Takagi–Sugeno (T-S) fuzzy delayed Hopfield neural networks. By employing a suitable Lyapunov–Krasovskii functional, a delay-dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is asymptotically stable. It is shown that the design of the proposed state estimator for such neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

A Scaling Parameter Approach to Delay-Dependent State Estimation of Delayed Neural Networks

This brief is concerned with studying the delay-dependent state estimation problem of recurrent neural networks with time-varying delay. The neuron activation function is more general than the sigmoid functions, and the time-varying delay is allowed to vary fast with time. A scaling parameter based approach is proposed, and a delay-dependent criterion is derived under which the resulting error system is globally asymptotically stable. It is shown that the design of a proper state estimator is directly accomplished by means of the feasibility of a linear matrix inequality. Thanks to the introduction of a scaling parameter, the developed result can efficiently be applied to chaotic delayed neural networks.

Robust $D$-Stability for a Class of Complex Singularly Perturbed Systems

This brief is concerned with the robust D-stability problem for a class of complex singularly perturbed systems with state delay. According to singular system approach, sufficient conditions, which are tested easily, are obtained by introduce delay-dependent state feedback, to ensure that the two-time-scale systems are regular, impulse free and D -stable, that is, all its poles are located with a specified disk for all small positive parameter epsiv isin (0,epsiv*) .

Time-Multiplied Guaranteed Cost Control of Linear Delay Systems

This paper investigates the design of guaranteed cost controllers for a class of linear systems with a state delay using a time-multiplied linear quadratic cost function. Based on delay-dependent and delay-independent stability criteria, guaranteed cost controllers can be constructed via solutions to linear matrix inequalities (LMIs) such that the resulting closed-loop system is stable and a specified time-multiplied linear integral-quadratic cost function has an upper bound. By the cone complementary linearization method, delay-dependent state feedback controllers can be derived in terms of LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators

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.

Design of exponential state estimator for neural networks with distributed delays

In this letter, the delay-dependent state estimation problem for recurrent neural networks with both time-varying and distributed time-varying delays is investigated. Through available output measurements, a delay-dependent criterion is established to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable. The derivative of a time-varying delay can take any value and the activation functions are assumed to be neither monotonic, nor differentiable, which are more general than the recently commonly used Lipschitz conditions. Finally, two illustrative examples are given to demonstrate the usefulness of the obtained condition.

Exponential state estimation for recurrent neural networks with distributed delays

In this paper, the delay-dependent state estimation problem for recurrent neural networks with both time-varying and distributed time-varying delays is investigated. Through available output measurements, a delay-dependent criterion is established to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable. The derivative of a time-varying delay satisfies τ ˙ ( t ) ⩽ μ and the activation functions are assumed to be neither monotonic nor differentiable, and more general than the recently commonly used Lipschitz conditions. Finally, two illustrative examples are given to demonstrate the usefulness of the obtained condition.

An LMI approach to delay-dependent state estimation for delayed neural networks

This paper is concerned with the state estimation problem for a class of neural networks with time-varying delay. Comparing with some existing results in the literature, the restriction such as the time-varying delay was required to be differentiable or even its time-derivative was assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. A delay-dependent condition is developed to estimate the neuron states through observed output measurements such that the error-state system is globally asymptotically stable. The criterion is formulated in terms of linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An example with simulation results is given to illustrate the effectiveness of the proposed result and the improvement over the existing ones.

Delayed fuzzy control of a unified chaotic system

In this paper, we have studied a new delay-dependent chaos control approach via delayed state feedback. This approach uses Takagi-Sugeno fuzzy model to represent a unified chaotic system and adopts the theory of Lyapunov-Krasovskii stability and linear matrix inequalities (LMIs). Simulation results show that the delay-dependent state feedback controller we designed can stabilize the unified chaotic system to its equilibrium.

H ∞ state feedback delay-dependent control for discrete systems with multi-time-delay

In this paper, H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.

H∞ disturbance attenuation for state delayed systems

In this note, the differential game and dissipation inequality are applied to the disturbance attenuation or H ∞-control for linear systems with delayed state. Firstly, a simple sufficient condition on the existence of a γ-suboptimal H ∞ state feedback controller is given, which is independent of delay, and an observer-based dynamic output feedback solution is presented in terms of Riccati inequalities (or Riccati equations). Secondly, a sufficient condition on the existence of a delay-dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods.