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This paper considers the boundary stabilization of stochastic delay reaction-diffusion systems(SDRDSs). We present the integral-form Lyapunov stability lemma for SDRDSs which provides the foundation of stability analysis for stochastic reaction-diffusion systems. Then, we design a boundary controller and obtain a criterion to guarantee the globally stochastically asymptotical stability of SDRDSs with...
This paper deals with stability of time delayed Takagi-Sugeno (TS) fuzzy systems. By considering a linear function which bound the derivative of fuzzy weighting functions, a relaxed stability method is established. A new stability approach is derived for time delayed TS systems by using integral Lyapunov function. To show the advantages of the proposed approaches, an illustrative example is given.
We prove a new extension of Razumikhin's theorem that applies to time-varying nonlinear systems with time-varying delays, using a novel ‘strictification’ method for converting a nonstrict Lyapunov function into a strict Lyapunov function. We apply our method to a model from identification theory, to illustrate how our new result can allow broader classes of delays than earlier methods.
In this paper, the problem of finite-time stabilization of stochastic delay reaction-diffusion systems (SDRDSs) is investigated. The finite-time controller is designed without using the sign function. Then, applying the stochastic finite-time stability lemma, utilizing Lyapunov-Krasoviskii functional method and Itö formula, a sufficient condition is derived which guarantees the finite-time stabilization...
We present a new backstepping result for control affine time-varying systems with input delays. The novelty of our work is in the bounds on the controls, and the facts that (i) one does not need to compute any Lie derivatives to apply our controls and (ii) the controls have no distributed terms.
This paper addresses output feedback stabilization of fully actuated rigid-body attitude dynamics in the presence of unknown point-wise time-delay in the input torque. Specifically, rate-gyros are unavailable here and only the attitude state represented by the unit quaternion is assumed to be measured. In the absence of time-delay, it is well known that linear asymptotically stabilizing control laws...
This paper focuses on the static output feedback stabilization problem for a class of SISO systems in the case of multiple delay controllers. We are interested in giving necessary conditions for the existence of such stabilizing controllers. Illustrative examples (a chain of integrators, or a chain of oscillators) are presented and discussed.
Lévy noise has been employed to stabilize the differential delay system, which have generalized the Brownian motion case, and we deal with the inevitable delay problem. The sufficient conditions of stabilization and destabilization have been given in the main results, and we discuss the reasons of increasing conservatism in the final section of the paper.
The reduction model approach is useful for stabilizing linear systems with arbitrarily long input delays. Here we adapt the approach to time varying nonlinear systems whose nonlinear parts satisfy certain structural conditions. We use Lyapunov-Krasovskii functionals to prove local stability of the closed loop systems. We provide estimates of the basins of attraction, and cover uncertainties acting...
This paper generalizes the Small Gain Theorem - SGT to cope with time-delay switched linear systems. The main purpose is to obtain delay-dependent stability conditions that can be imposed by means of an appropriate switching strategy. Both cases of switching strategies corresponding to state and output feedback are considered. The new version of SGT is specially important in the framework of switched...
For networked systems, the control law is typically subject to network flaws such as delays and packet dropouts. Hence, the time in between updates of the control law varies unexpectedly. Here, we present a stability theorem for nonlinear model predictive control with varying control horizon in a continuous time setting without stabilizing terminal constraints or costs. It turns out that stability...
We consider a large class of fractional delay systems with many neutral chains of poles approaching a same set of points on the imaginary axis. As a primary work regarding H∞-stability analysis, high modulus poles of neutral chains are approximated.
This paper proposes a novel self-triggered sampling scheme for the execution of sampling in networked control systems by taking into consideration network-induced delays and data packet dropouts. Using this scheme, the next sampling period is dynamically obtained with respect to (a) the desired performance; (b) the latest accepted time-stamped control packet; and (c) the allowable communication delay...
We consider a general class of distributed algorithms for the control of power allocations in time-dependent wireless networks. We employ appropriately constructed Lyapunov functions to show that any bounded power distribution obtained from these algorithms is uniformly asymptotically stable. Further, we use Lyapunov-Razumikhin functions to show that even when the system incorporates heterogeneous,...
The input-to-state stability (ISS) property is combined with model predictive control (MPC) of systems with time-delays and disturbances. We derive conditions such that an MPC scheme assures ISS for a single system and each subsystem of a network. To this end, it is shown that the cost functionals of the used MPC scheme are ISS-Lyapunov-Krasovskii functionals. Recent results of the stability analysis...
This paper investigates the problem of mean-square asymptotic stability of uncertain neural networks with time-varying delay and stochastic noise. Based on generalized Finsler lemma and the linear matrix inequality (LMI) optimization technique, an improved delay-dependent stability criterion is developed. It is shown that the new stability criterion is less conservative and less computationally complex...
In this paper, the Genesio system with distributed time delay feedback is studied. Its linear stability is investigated based on the Routh-Hurwitz criteria. After the local asymptotic stability is analyzed, Hopf bifurcation is demonstrated by choosing the mean time delay as a bifurcation parameter. The direction and the stability criteria of the bifurcating periodic solutions are determined by applying...
In this paper, some sufficient conditions for global robust asymptotical stability of neural networks with time-varying delays are presented. On basis of the obtained results, some linear matrix inequality (LMI) criteria are derived. A comparison of the present criteria with the previous criteria is made. Moreover, an example is given to show the effectiveness of the obtained results.
This paper investigated the stabilization and stability problems for the Takagi-Sugeno (T-S) fuzzy systems with delays in state and input. Based on the non-parallel distributed compensation (non-PDC) technology, a fuzzy controller with non-PDC control laws is proposed to stabilize the T-S fuzzy systems with delays in state and input. For relaxing the stabilization conditions, a parameter-dependent...
Stability analysis and control for linear periodic time-delay systems described by state space models are investigated in this paper. Semi-discretization method is used to develop a mapping of the system response in a finite-dimensional state space. The stability region and stability boundary can be found by comparing the maximum absolute value of the mapping's eigenvalues with 1. More importantly,...
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