In this paper, a new impulsive delay inequality that involves unbounded and nondifferentiable time-varying delay is presented. As an application, some sufficient conditions ensuring stability and ...stabilization of impulsive systems with unbounded time-varying delay are derived. Some numerical examples are given to illustrate the results. Especially, a stabilizing memoryless controller for a second-order time-varying system with unbounded time-varying delay is proposed.
To analyze the delay-dependent stability of a load frequency control (LFC) system with transmission delays, the continuous-time model with delay is usually adopted. However, practical LFC is actually ...a sampled-data system, where the power commands sent to generation units are updated every few seconds. It is therefore desirable to analyze the delay-dependent stability of LFC when sampling is introduced. This paper undertakes stability analysis of LFC with both sampling and transmission delay. The model of the LFC system is first modified to consider sampling and transmission delay separately. Based on Lyapunov stability theory and linear matrix inequalities, a new stability criterion for linear systems with both sampling and transmission delay is proposed using the Wirtinger-based integral inequality and its affine version. The proposed criterion is applicable for both time-invariant and time-varying transmission delays. Case studies are undertaken on both single-area and two-area LFC systems to verify the effectiveness and advantage of the proposed method.
The use of unmanned aerial vehicles (UAVs) as communication platforms is of great significance in future wireless networks, especially for on-demand deployment in temporary events and emergency ...situations. Although prior works have shown the performance improvement by exploiting the UAV's mobility, they mainly focus on delay-tolerant applications. As delay requirements fundamentally limit the UAV's mobility, it remains unknown whether the UAV is able to provide any performance gain in delay-constrained communication scenarios. Motivated by the above, we study, in this paper, an UAV-enabled orthogonal frequency-division multiple access (OFDMA) network where an UAV is dispatched as the mobile base station (BS) to serve a group of users on the ground. We consider a minimum-rate ratio (MRR) for each user, defined as the minimum instantaneous rate required over the average achievable throughput, to flexibly adjust the percentage of its delay-constrained data traffic. Under a given set of constraints on the users' MRRs, we aim to maximize the minimum average throughput of all users by jointly optimizing the UAV trajectory and OFDMA resource allocation. First, we show that the max-min throughput in general decreases as the users' MRRs become larger, which reveals a fundamental throughput-delay tradeoff in UAV-enabled communications. Next, we propose an iterative parameter-assisted block coordinate descent method to optimize the UAV trajectory and OFDMA resource allocation alternately, by applying the successive convex optimization and the Lagrange duality, respectively. Furthermore, an efficient and systematic UAV trajectory initialization scheme is proposed based on the simple circular trajectory. Finally, simulation results are provided to verify our theoretical findings and demonstrate the effectiveness of our proposed designs.
This paper concerns the delay margin achievable using proportional-integral-derivative (PID) controllers for linear time-invariant (LTI) systems subject to variable, unknown time delays. The basic ...issue under investigation addresses the question: What is the largest range of time delay so that there exists a single PID controller to stabilize the delay plants within the entire range? Delay margin is a fundamental measure of robust stabilization against uncertain time delays and poses a fundamental, longstanding problem that remains open except in simple, isolated cases. In this paper, we develop explicit expressions of the exact delay margin and its upper bounds achievable by a PID controller for low-order delay systems, notably the first- and second-order unstable systems with unknown constant and possibly time-varying delays. The effect of nonminimum phase zeros is also examined. PID controllers have been extensively used to control and regulate industrial processes that are typically modeled by first- and second-order dynamics. While furnishing the fundamental limits of delay within which a PID controller may robustly stabilize a delay process, our results should also provide useful guidelines in tuning PID parameters and in the analytical design of PID controllers.
Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in delay-Doppler channels. In ...order to detect OTFS modulated data, the channel impulse response needs to be known at the receiver. In this paper, we propose embedded pilot-aided channel estimation schemes for OTFS. In each OTFS frame, we arrange pilot, guard, and data symbols in the delay-Doppler plane to suitably avoid interference between pilot and data symbols at the receiver. We develop such symbol arrangements for OTFS over multipath channels with integer and fractional Doppler shifts, respectively. At the receiver, channel estimation is performed based on a threshold method and the estimated channel information is used for data detection via a message passing algorithm. Thanks to our specific embedded symbol arrangements, both channel estimation and data detection are performed within the same OTFS frame with minimum overhead. We compare through simulations the error performance of OTFS using the proposed channel estimation and OTFS with ideally known channel information and observe only a marginal performance loss. We also demonstrate that the proposed channel estimation in OTFS significantly outperforms OFDM with known channel information. Finally, we present extensions of the proposed schemes to multiple-input multiple-output (MIMO) and multi-user uplink/downlink.
The strong delay-independent stability (DIS) of linear time-invariant retarded multiple time-delay systems (MTDS) is studied in the entire delay space. We develop a new one-step discriminant approach ...utilizing the generalized Dixon resultant, which unveils the necessary and sufficient algebraic condition for the upper frequency bound. The lower frequency bound is rigorously ascertained by further inspecting the zero spectrum. Then, we raise seven postulates concerning the system stability state for the strong DIS analysis, which are examined by four independent stability criteria. Additionally, we integrate the Gaussian elimination-based rank subdeterminant calculation into our algorithm to deal with the degenerate resultant operator. Finally, we prove that our one-step approach is more uniform, automatic, and efficient compared to the iterated discriminant approach with successive Sylvester resultant computations, especially when tackling a complicated MTDS with more than two delays. Several example cases are provided.
This article studies the local finite-time stability for a class of time-delay systems. Some Lyapunov-based sufficient conditions are proposed in the framework of finite time, where a potential ...connection between time delay and system parameters for local finite-time stability is established. An estimate of the upper bound of the settling time depending on the time delay is derived. Examples are given to illustrate the effectiveness of the proposed results. Especially, a finite-time stabilizing memoryless controller for a class of second-order systems with time-varying delay is proposed.
This paper investigates the problem of robust H a fuzzy control for a class of uncertain nonlinear Markovian jump systems with time-varying delay. The class of systems under consideration is ...described by the Takagi-Sugeno fuzzy model. The goal of the paper is to design a mode-dependent fuzzy state-feedback controller such that the closed-loop system is stochastically stable with a prescribed H a performance of disturbance attenuation for all admissible parameter uncertainties. In order to obtain a less conservative control design, a new stochastic LyapunovaKrasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals. Then, by employing this functional, a delay decomposition approach to the design of robust H a fuzzy controllers is developed in terms of linear matrix inequalities. Finally, two examples are given to illustrate the merit and usability of the proposed design method.
The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use ...of a model transformation and the technique of bounding cross terms. This technical note presents a new integral inequality, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods. It includes well-known integral inequalities as special cases. Using it to investigate the stability of systems with time-varying delays yields less conservative delay-dependent stability criteria, which are given in terms of linear matrix inequalities. Two numerical examples demonstrate the effectiveness and superiority of the method.
This article is concerned with the local stabilization problem for discrete-time systems with both distributed state delay and fast-varying input delay under actuator saturations. By introducing some ...terms concerning the distributedly delayed state and the current state, a novel polytopic model is first proposed to characterize the delayed saturation nonlinearity. Then, by incorporating a piecewise Lyapunov functional and some summation inequalities, a sufficient condition is established by means of linear matrix inequalities under which the closed-loop system is locally exponentially stable. Moreover, the conditions for two special cases with single state delay and single input delay are proposed. Subsequently, certain optimization problems are formulated with aim to maximize the estimate of the region of attraction. Finally, two examples show the effectiveness and values of the obtained results.
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