Delay-dependent approach to robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties

A delay-dependent approach to robust H _∞ filtering is proposed for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties. The delays are interval time-varying delays and uncertainties are a convex compact set of polytopic types. The aim of the designed filter is to guarantee regular, causal, asymptotic stability with H _∞ norm bound of filtering error singular systems. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded lemma (BL) for singular systems with interval time-varying delays is proposed. Based on the result, the existence condition of the robust H _∞ filter and the filter design method are presented in terms of linear matrix inequality (LMI). Finally, two examples are also given to illustrate the effectiveness of the proposed methodology.     

New delay-interval stability condition

The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r,?τ]. The case of unstable delayed systems for r?=?0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.     

Memoryless H ∞ controller design for switched non-linear systems with mixed time-varying delays

This article deals with the H _∞ control problem for a class of switched non-linear systems with mixed time-varying delays. The novel features here are that the system in consideration is non-linear perturbation with discrete and distributed delays, the time-varying delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using Lyapunov–Razumikhin functional approach, new sufficient conditions for the H _∞ control with exponential stability constraint are derived in terms of the solution of Riccati-type equations. The approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution.     

Improved H ∞ analysis of Markovian jumping stochastic systems with time-varying delays

This article investigates the problems of H _∞ analysis for Markovian jump stochastic systems with both nonlinear disturbance and time-varying delays. By virtue of the delay partition approach, the improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian jump stochastic systems are obtained in terms of linear matrix inequalities (LMIs). The proposed approach involves neither free weighting matrices nor any model transformation, and it is shown that the new criteria have the capability of providing less conservative results than the state-of-the-art. Two numerical simulations are conducted to demonstrate the effectiveness of the proposed method in comparison with existing methods.     

Stability of systems with uncertain delays: a new "Complete" Lyapunov-krasovskii functional

Stability of linear systems with uncertain time-varying delay is considered in the case, where the nominal value of the delay is constant and nonzero. Recently a new construction of Lyapunov-Krasovskii functionals (LKFs) has been introduced: To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturbed system and that vanish when the delay perturbations approach 0. In the present note we combine a "complete" nominal LKF, the derivative of which along the trajectories depends on states and their derivatives, with the additional terms depending on the delay perturbation. The new method is applied to the case of multiple uncertain delays with one nonzero nominal value. Numerical examples illustrate the efficiency of the method.     

Stability analysis of uncertain neutral systems with discrete and distributed delays via the delay partition approach

This paper focuses on the stability analysis for neutral systems with discrete and distributed constant time-delays. Lyapunov-Krasovskii functionals (LKFs) are constructed by non uniformly dividing the whole delay interval into multiple segments and choosing proper functionals with different weighting matrices coressponding to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the neutral system in the delay partition approach. By utilizing the delay partition approach, the obtained stability criteria are stated in terms of linear matrix inequalities. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed approach less conservative than the existing ones.     

Input–output approach to stability and -gain analysis of systems with time-varying delays

Stability and L₂ (l₂)-gain of linear (continuous-time and discrete-time) systems with uncertain bounded time-varying delays are analyzed under the assumption that the nominal delay values are not equal to zero. The delay derivatives (in the continuous-time) are not assumed to be less than q<1. An input–output approach is applied by introducing a new input–output model, which leads to effective frequency domain and time domain criteria. The new method significantly improves the existing results for delays with derivatives not greater than 1, which were treated in the past as fast-varying delays (without any constraints on the delay derivatives). New bounded real lemmas (BRLs) are derived for systems with state and objective vector delays and norm-bounded uncertainties. Numerical examples illustrate the efficiency of the new method.     

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

     

On stability and stabilisation for uncertain stochastic systems with time-delay and actuator saturation

This article concerns the stability analysis and design for uncertain stochastic systems with time-varying delays in state and actuator saturation. The parameter uncertainties belong to a convex polytopic set, and the delays are time varying. A sufficient condition is obtained in terms of a priori designed feedback matrix for determining if a given set is in inside the domain of attraction. Using the linear matrix inequality (LMI) approach, an estimate of the domain of attraction is presented. The problem of designing a state feedback controller such that the domain of attraction is enlarged is formulated through solving an optimisation problem with LMI constraints. A numerical example is given to illustrate the effectiveness of the proposed results.     

Stability analysis of systems via a new double free-matrix-based integral inequality with interval time-varying delay

ABSTRACT

This paper investigates the problem of delay-dependent stability analysis for systems with interval time-varying delay. By means of a new double free-matrix-based integral inequality and augmented Lyapunov–Krasovskii functionals containing as much information of time-varying delay as possible, a new stability criterion for systems is established. Firstly, by a double integral term two-step estimation approach and combined with single free-matrix-based integral inequalities, a stability criteria is presented. Then, compared with the double integral term two-step estimation approach, the proposed new double free-matrix-based integral inequality with more related time delays has potential to lead to a criterion with less conservatism. Finally, the validity of the presented method is demonstrated by two numerical examples.     

New results on H ∞ filter design for nonlinear systems with time-delay through a T-S fuzzy model approach

H _∞ filter design for nonlinear systems with time-delay via a T-S fuzzy model approach is investigated based on a piecewise analysis method. Two cases of time-varying delays are fully considered: one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with delay-derivative bounded by a constant. Based on a piecewise analysis method, the variation interval of the time delay is first divided into several subintervals, then the convexity property of the matrix inequality and the free weighting matrix method are fully used in this article. Some novel delay-dependent H _∞ filtering criteria are expressed as a set of linear matrix inequalities, which can lead to much less conservative analysis results. Finally, a numerical example is given to illustrate that the results in this article are more effective and less conservative than some existing ones.     

Event-based H2/H∞ controllers for networked control systems

This paper is concerned with event-based H₂/H_∞ control design for networked systems with interval time-varying delays. The contributions are twofold. First, conditions for uniform ultimately bounded stability are provided in the H₂/H_∞ event-based context. The relation between the boundedness of the stability region and the threshold that triggers the events is studied. Second, a practical design procedure for event-based H₂/H_∞ control is provided. The method makes use of Lyapunov–Krasovskii functionals (LKFs) and it is characterised by its generality, as only mild assumptions are imposed on the structures of the LKF and the cost functional. The robustness and performance of the proposed technique is showed through numerical simulations.     

On ℓ∞ and L∞ gains for positive systems with bounded time-varying delays

This paper is devoted to the analysis of the ?_∞ and L_∞ gains for positive linear systems with interval time-varying delays. Through exploiting the monotonicity of the state trajectory, we first prove that for positive systems with constant delays, the ?_∞ and L_∞ gains are fully governed by the system matrices but independent of the delay size. Moreover, for positive systems with bounded time-varying delays, by comparing with the nominal systems with constant delays, it turns out that the ?_∞ and L_∞ gains are exactly the same as that of the constant delay systems. The results in this paper reveal that the ?_∞ and L_∞ gains of positive linear systems are not sensitive to the magnitude of time delays and hence the computation of ?_∞ and L_∞ gains of positive systems with bounded time-varying delays can be reduced to computing the ?_∞ and L_∞ gains of the corresponding delay-free systems. Both continuous-time and discrete-time cases are considered in this paper.     

Delay Dependent Exponential Stability for Fuzzy Recurrent Neural Networks with Interval Time-Varying Delay

In this paper, the problem of delay-dependent exponential stability for fuzzy recurrent neural networks with interval time-varying delay is investigated. The delay interval has been decomposed into multiple non equidistant subintervals, on these interval Lyapunov-Krasovskii functionals (LKFs) are constructed to study stability analysis. Employing these LKFs, an exponential stability criterion is proposed in terms of Linear Matrix Inequalities (LMIs) which can be easily solved by MATLAB LMI toolbox. Numerical example is given to illustrate the effectiveness of the proposed method.     

Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay

The objective of this paper is to analyze the stability analysis of neutral-type neural networks with additive time-varying delay and leakage delay. By constructing a suitable augmented Lyapunov-Krasovskii functional with triple and four integral terms, some new stability criteria are established in terms of linear matrix inequalities, which is easily solved by various convex optimization techniques. More information of the lower and upper delay bounds of time-varying delays are used to derive the stability criteria, which can lead less conservative results. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasible can be checked easily by MATLAB LMI control toolbox. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

     

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

The exponential string stability for a class of nonlinear interconnected large-scale systems with time-varying delay is analysed by using the box theory and constructing a vector Lyapunov function. Under the assumption that the time delay is bounded and continuous, a criterion for exponential string stability of the systems is obtained by analysing the stability of differential inequalities with time-varying delay. The large-scale system is exponential string stable when the conditions associating with the coefficient matrices of the system and the solutions of the Lyapunov equations, interconnected with the system, are satisfied. Since it is independent of the delays and simplifies the calculation, the criterion is easy to apply.     

Further improvement of stability criterion and BRL for Markovian jump systems with interval time-varying delay

This paper deals with delay-dependent stochastic stability and bounded real lemma(BRL)for Markovian jump linear systems with interval time-varying delays.By constructing some new Lyapunov functionals and using the Jensen’s integral inequality method,the free weighting matrix method,the convex combination method and the delay decomposition approach integratedly,some less conservative delay-dependent stability criteria and BRL are established. Numerical examples are given to show the effectiveness of the proposed method.     

Impulsive control of unstable neural networks with unbounded time-varying delays

This paper considers the impulsive control of unstable neural networks with unbounded time-varying delays, where the time delays to be addressed include the unbounded discrete time-varying delay and unbounded distributed time-varying delay. By employing impulsive control theory and some analysis techniques, several sufficient conditions ensuring μ-stability, including uniform stability, (global) asymptotical stability, and (global) exponential stability, are derived. It is shown that an unstable delay neural network, especially for the case of unbounded time-varying delays, can be stabilized and has μ-stability via proper impulsive control strategies. Three numerical examples and their simulations are presented to demonstrate the effectiveness of the control strategy.     

Predictor-based control of linear systems with large and variable measurement delays

This paper concerns the problem of the control of linear systems by means of feedback from delayed output, where the delay is known and time-varying. The main advantage of the approach is that it can be applied to systems with any delay bound, i.e. not only small delays. The predictor is based on a combination of finite-dimensional elementary predictors whose number can be suitably chosen to compensate any delay. The single-predictor element is an original proposal, and the class of delays to which the schema can be applied includes, but it is not limited to, continuous delay functions.