Robust Dissipativity Research Articles

Delay-dependent robust dissipativity conditions for delayed neural networks with random uncertainties

This paper deals with the problem of the robust dissipativity analysis for delayed neural networks with randomly occurring uncertainties. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli distributed white noise sequences. By using reciprocally convex approach combined with an extended Wirtinger inequality, some delay-dependent conditions for the concerned neural networks to be stochastically strictly (Q,S,R)-θ-dissipative are established. Finally, two numerical examples are given to illustrate the reduced conservatism and effectiveness of our proposed approach.

Global Robust Exponential Dissipativity for Interval Recurrent Neural Networks with Infinity Distributed Delays

This paper is concerned with the robust dissipativity problem for interval recurrent neural networks (IRNNs) with general activation functions, and continuous time-varying delay, and infinity distributed time delay. By employing a new differential inequality, constructing two different kinds of Lyapunov functions, and abandoning the limitation on activation functions being bounded, monotonous and differentiable, several sufficient conditions are established to guarantee the global robust exponential dissipativity for the addressed IRNNs in terms of linear matrix inequalities (LMIs) which can be easily checked by LMI Control Toolbox in MATLAB. Furthermore, the specific estimation of positive invariant and global exponential attractive sets of the addressed system is also derived. Compared with the previous literatures, the results obtained in this paper are shown to improve and extend the earlier global dissipativity conclusions. Finally, two numerical examples are provided to demonstrate the potential effectiveness of the proposed results.

Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties

This paper investigates the problem of ro- bust dissipativity analysis for uncertain neural net- works with time-varying delay. The norm-bounded uncertainties enter into the neural networks in ran- domly ways, and such randomly occurring uncer- tainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. By em- ploying the linear matrix inequality (LMI) approach, a sufficient condition is established to ensure the robust stochastic stability and dissipativity of the considered neural networks. Some special cases are also consid- ered. Two numerical examples are given to demon- strate the validness and the less conservatism of the obtained results.

An LMI approach for global robust dissipativity analysis of T–S fuzzy neural networks with interval time-varying delays

Takagi–Sugeno (T–S) fuzzy models are often used to represent complex nonlinear systems by means of fuzzy sets and fuzzy reasoning applied to a set of linear sub-models. In this paper, the global robust dissipativity of T–S fuzzy neural networks with interval time-varying delays are investigated. By constructing a proper Lyapunov–Krasovskii functional and using linear matrix inequality (LMI) technique, delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of fuzzy neural networks have been derived in terms of LMI, which can be solved numerically using LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.

Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov–Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties . This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests . The developed results in this paper for the nominal system encompass available results on H ∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.

Global robust point dissipativity of interval neural networks with mixed time-varying delays

In this paper, the global robust point dissipativity of an uncertain neural networks model with mixed time-varying delays is investigated, based on Lyapunov theory and inequality techniques. First, the concept of global robust point dissipativity is introduced. Next, some sufficient conditions are given for checking the global robust point dissipativity and the global exponential robust dissipativity of the uncertain neural networks model. Finally, illustrated examples are given to show the effectiveness of our results.

Robust dissipativity of discrete systems and its investigation with the help of a sequence of sets of Lyapunov functions

A generalized concept of robust dissipativity is introduced and theorems on the analysis of this property are formulated and proved with the help of the Lyapunov functions method. It is proposed to use a specially constructed sequence of sets of Lyapunov functions that can allow one to improve the initial estimate of the boundary set of a dissipative system up to the establishment of the asymptotic robust stability property in the limiting case. An example of investigating the dissipativity of a linear discrete system with unknown parameters under additive perturbation is given.

A robust semi-definite optimization based solution to the robust order reduction problem for parametric uncertain dissipative linear systems

In this paper, we address the problem of reducing the order of a linear system affected by uncertainties from the robust dissipative perspective introduced in Barb et al. (2003, Robust dissipativity of interval uncertain linear systems. SIAM J. Control Optim., 41, 1661–1695.). First, we show that all major balanced truncation techniques developed and reported in the literature of the last two decades can be treated in a uniform fashion within the framework of dissipative systems. Accordingly, we shall generalize these results to uncertain dissipative systems. The key role is played by balancing two positive definite robust solutions to the uncertain dissipativity linear matrix inequalities (LMIs) associated with the linear system in question and its dual. Determining the maximal level of uncertainty for which such two solutions exist and computing them efficiently is well known to be non-poly NP-hard. Our method is based on determining robust tractable approximations of these NP-hard entities by following the novel method known as Matrix-Cube theory. The proven results are accompanied by a numerical example.

Global robust dissipativity for integro-differential systems modeling neural networks with delays

In this paper, the global robust dissipativity of integro-differential systems modeling neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are the global robust dissipativity. The results are shown to improve the previous global dissipativity results derived in the literature. Some examples are given to illustrate the correctness of our results.

Robust dissipativity for uncertain impulsive dynamical systems

We discuss the robust dissipativity with respect to the quadratic supply rate for uncertain impulsive dynamical systems. By employing the Hamilton‐Jacobi inequality approach, some sufficient conditions of robust dissipativity for this kind of system are established. Finally, we specialize the obtained results to the case of uncertain linear impulsive dynamical systems.

Robust Dissipativity of Interval Uncertain Linear Systems

In this paper we are concerned with the problem of robust dissipativity of linear systems with parameters affected by box uncertainty; our major goal is to evaluate the largest uncertainty level for which all perturbed instances share a common dissipativity certificate. While it is NP-hard to compute this quantity exactly, we demonstrate that under favorable circumstances one can build an O(1)-tight lower bound of this "intractable" quantity by solving an explicit semidefinite program of the size polynomial in the size of the system. We consider a number of applications, including the robust versions of the problems of extracting nearly optimal available storage, providing nearly optimal required supply, Lyapunov stability analysis, and linear-quadratic control.