New results on robust exponential stability of integral delay systems

"The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov–Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.

On Asymptotic Stability of Stochastic Differential Equations with Delay in Infinite Dimensional Spaces

In most stochastic dynamical systems which describe process in engineering, physics and economics, stochastic components and random noise are often involved. Stochastic effects of these models are often used to capture the uncertainty about the operating systems. Motivated by the development of analysis and theory of stochastic processes, as well as the studies of natural sciences, the theory of stochastic differential equations in infinite dimensional spaces evolves gradually into a branch of modern analysis. In the analysis of such systems, we want to investigate their stabilities. This thesis is mainly concerned about the studies of the stability property of stochastic differential equations in infinite dimensional spaces, mainly in Hilbert spaces. Chapter 1 is an overview of the studies. In Chapter 2, we recall basic notations, definitions and preliminaries, especially those on stochastic integration and stochastic differential equations in infinite dimensional spaces. In this way, such notions as Q-Wiener processes, stochastic integrals, mild solutions will be reviewed. We also introduce the concepts of several types of stability. In Chapter 3, we are mainly concerned about the moment exponential stability of neutral impulsive stochastic delay partial differential equations with Poisson jumps. By employing the fixed point theorem, the p-th moment exponential stability of mild solutions to system is obtained. In Chapter 4, we firstly attempt to recall an impulsive-integral inequality by considering impulsive effects in stochastic systems. Then we define an attracting set and study the exponential stability of mild solutions to impulsive neutral stochastic delay partial differential equations with Poisson jumps by employing impulsive-integral inequality. Chapter 5 investigates p-th moment exponential stability and almost sure asymptotic stability of mild solutions to stochastic delay integro-differential equations. Finally in Chapter 6, we study the exponential stability of neutral impulsive stochastic delay partial differential equations driven by a fractional Brownian motion

Robust Compensation of Delay and Diffusive Actuator Dynamics Without Distributed Feedback

[EN] This paper deals with robust observer-based output-feedback stabilization of systems whose actuator dynamics can be described in terms of partial differential equations (PDEs). More specifically, delay dynamics (first-order hyperbolic PDE) and diffusive dynamics (parabolic PDE) are considered. The proposed controllers have a PDE observer-based structure. The main novelty is that stabilization for an arbitrarily large delay or diffusion domain length is achieved, while distributed integral terms in the control law are avoided. The exponential stability of the closed loop in both cases is proved using Lyapunov functionals, even in the presence of small uncertainties in the time delay or the diffusion coefficient. The feasibility of this approach is illustrated in simulations using a second-order plant with an exponentially unstable mode.This work was supported in part by Project TIN2017-86520-C3-1-R, Ministerio de Economia y Competitividad, in part by the 16/17 UPV Mobility Award, and in part by the FPI-UPV 2014 Ph.D. Grant, Universitat Politecnica de Valencia, Spain.Sanz Diaz, R.; García Gil, PJ.; Krstic, M. (2019). Robust Compensation of Delay and Diffusive Actuator Dynamics Without Distributed Feedback. IEEE Transactions on Automatic Control. 64(9):3663-3675. https://doi.org/10.1109/TAC.2018.2887148S3663367564

On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations

In this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness theorem as well as the almost surely asymptotic behavior for the global solution of highly nonlinear stochastic differential equations with time-varying delay and Markovian switching are discussed by using the Lyapunov function and some stochastic analysis techniques. Two integral lemmas are firstly established to overcome the difficulty stemming from the coexistence of the stochastic perturbation and the time-varying delay. Then, without any redundant restrictive condition on the time-varying delay, by utilizing the integral inequality, the exponential stability in pth(p ≥ 1)-moment for such equations is investigated. By employing the nonnegative semi-martingale convergence theorem, the almost sure exponential stability is analyzed. Finally, two examples are given to show the usefulness of the results obtained.National Natural Science Foundation of ChinaNatural Science Foundation of Jiangxi Province of ChinaFoundation of Jiangxi Provincial Educations of ChinaMinisterio de Economía y Competitividad (MINECO). EspañaJunta de Andalucí

Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument

We consider a new model for shunting inhibitory cellular neural networks, retarded functional differential equations with piecewise constant argument. The existence and exponential stability of almost periodic solutions are investigated. An illustrative example is provided.Comment: 24 pages, 1 figur

Stability Analysis of Integral Delay Systems with Multiple Delays

This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.Comment: 14 page

Integration of continuous-time dynamics in a spiking neural network simulator

Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here supports the combination of the two for multi-scale modeling approaches, the quantitative validation of mean-field approaches by spiking network simulations, and an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most efficient spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. We further demonstrate the broad applicability of the framework by considering various examples from the literature ranging from random networks to neural field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation