This technical note is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the technical note comes from the consideration of a new inequality ...which is less conservative than the celebrated Jensen inequality employed in the context of discrete-time delay systems. This inequality is a discrete-time counterpart of the Wirtinger-based integral inequality that was recently employed for the improved analysis of continuous-tine systems with delays. However, differently from the continuous-time case, the proof of the new inequality is not based on the Wirtinger inequality. The method is also combined with an efficient representation of the improved reciprocally convex combination inequality in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.
This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the ...appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper.
Time delays exist in network-connected systems. Especially for vision-based multirobot systems, time delays are diverse and complicated due to the communication network, camera latency, image ...processing, etc. At the same time, many tasks, such as searching and rescue, have timing requirement. This paper focuses on fixed-time formation control of multirobot systems subject to delay constraints. First, predictor-based state transformation is employed for each robot to deal with the input delay, and the uncertain terms remained in the transformed systems are carefully considered. Then, a couple of nonlinear fixed-time formation protocols are proposed for the multirobot systems with respectively undirected and directed topology, and the corresponding settling time is derived by using the Lyapunov functions. In particular, the upper-bound estimation of the formation settling time is explicitly given irrelevant to the initial conditions. Finally, the protocols are validated through a numerical simulation example and then implemented on an E-puck robots platform. Both simulation and experimental results demonstrate the effectiveness of the proposed formation protocols.
An all-pass filter architecture that can be generalized to high orders, and can be realized using active circuits is proposed. Using this, a compact true-time-delay element with a widely tunable ...delay and a large delay-bandwidth product (DBW) is demonstrated. This is useful for beamforming and equalization in the lower GHz range where the use of LC or transmission line-based solutions to realize large delays is infeasible. Coarse tuning of delay is realized by changing the filter's order while keeping the bandwidth constant and fine tuning is implemented by changing the filter's bandwidth utilizing the delay-bandwidth tradeoff. A test chip fabricated in 0.13 μm CMOS process demonstrates a delay tuning range of 250 ps-1.7ns, over a bandwidth of 2 GHz, while maintaining a magnitude deviation of ±0.7 dB. The filter achieves a DBW of 3.4 and a delay per unit area of 5.8 ns/mm 2 . The filter has a worst case noise figure of 23 dB, and -40 dB intermodulation (IM3) distortion for 37 mVppd inputs. The chip occupies an active area of 0.6 mm 2 , and dissipates 112 mW-364 mW of power between its minimum and maximum delay settings. Computed radiation pattern with four antennas spaced λ fmax /2 apart shows ±90° beam steering off broadside.
This paper is concerned with global asymptotic stability of a neural network with a time-varying delay, where the delay function is differentiable uniformly bounded with delay-derivative bounded from ...above. First, a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions. This inequality provides a tighter bound in the form of a convex combination than some existing ones. Second, by constructing proper Lyapunov-Krasovskii functional, global asymptotic stability of the neural network is analyzed for two types of the time-varying delays depending on whether or not the lower bound of the delay derivative is known. Third, noticing that sufficient conditions on stability from estimation on the derivative of some Lyapunov-Krasovskii functional are affine both on the delay function and its derivative, allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study. Finally, two numerical examples are given to substantiate the effectiveness of the proposed method.
This paper studies the load frequency control (LFC) for power systems with communication delays via an event-triggered control method to reduce the amount of communications required. The effect of ...the load disturbances on the augmented output is defined as a robust performance index of the augmented LFC scheme. By utilizing a time-delayed system design approach, a new model of the LFC scheme with delays is formulated, where the communication delays and event-triggered control are integrated for the LFC scheme. Based on the Lyapunov-Krasovskii functional method, the criteria for the event-triggered stability analysis and control synthesis of the LFC scheme are derived. Finally, the effectiveness of the proposed method is verified by simulation studies.
Till now, there are lots of stability and stabilization results about Takagi-Sugeno (T-S) fuzzy systems with time delay, but most of them are independent of the analysis of membership functions. ...Since the membership functions are an essential component to make a fuzzy system different from others, the conditions without its information are conservative. In this brief paper, a new Lyapunov-Krasovskii functional is designed to investigate the stability and stabilization of continuous-time T-S fuzzy systems with time delay. Different from the existing results in the literature, the integrand of the Lyapunov-Krasovskii functional in this paper depends not only on the integral variable, but also on the membership functions, and thus, the information of the time derivative of membership functions can also be used to reduce the conservativeness of finding the maximum delay bounds. Utilizing the information of the time derivative of membership, a number of controllers are designed according to their sign, and then, a switching idea is applied to stabilize the fuzzy system. In the end, two examples are given to illustrate the feasibility and validity of the design and analysis.
The usage of communication channels introduces time delays into load frequency control (LFC) schemes. Those delays may degrade dynamic performance, and even cause instability, of a closed-loop LFC ...scheme. In this paper, a delay-dependent robust method is proposed for analysis/synthesis of a PID-type LFC scheme considering time delays. The effect of the disturbance on the controlled output is defined as a robust performance index (RPI) of the closed-loop system. At first, for a preset delay upper bound, controller gains are determined by minimizing the RPI. Secondly, calculation of the RPIs of the closed-loop system under different delays provides a new way to assess robustness against delays and estimate delay margins. Case studies are based on three-area LFC schemes under traditional and deregulated environments, respectively. The results show that the PID-type controller obtained can guarantee the tolerance for delays less than the preset upper bound and provide a bigger delay margin than the existing controllers do. Moreover, its robustness against load variations and parameter uncertainties is verified via simulation studies.
This paper proposes a distributed nonlinear consensus delay-dependent control algorithm for a connected vehicle (CV) platoon. In particular, considering that the behavior of the following vehicle is ...associated with the longitudinal inter-vehicle gap with respect to the preceding vehicle, a nonlinear function is designed to characterize the car-following interactions between CVs. Then, a nonlinear consensus algorithm is proposed by incorporating the car-following interactions and heterogeneous time delays. The delay-dependent convergence condition of the proposed control algorithm is analyzed using the Lyapunov-Krasovskii method, and an estimate of the delay bound is provided. Under the proposed algorithm, not only can the consensus of CVs be guaranteed but also the behavior of vehicles is consistent with traffic flow theory. Finally, an example using a 10-vehicle platoon is provided under three scenarios: no time delays, heterogeneous time delays, and homogeneous time delays. Results from extensive simulations verify the effectiveness of the proposed control algorithm in terms of the position, velocity, and acceleration/deceleration profiles.
Active disturbance rejection controller (ADRC) has achieved soaring success in motion controls featured by rapid dynamics. However, it turns obstreperous to implement it in the power plant process ...with considerable time-delay, largely because of the tuning difficulty. To this end, this article proposes a quantitative tuning rule for the time-delayed ADRC (TD-ADRC) structure based on the typical first order plus time delay (FOPTD) model. By compensating the FOPTD process as an integrator plus time delay in low frequencies, the gain parameter of TD-ADRC can be related to a scaled time constant which shapes the closed-loop tracking performance. Bandwidth parameter of extended state observer is scaled as a dimensionless parameter. A sufficient stability condition of TD-ADRC is theoretically derived in terms of the scaled parameter pair, the range of which falls within the practical interest. Relative delay margin is revealed as a critical robustness metric among others, a default pair of scaled parameter setting is recommended as well as an explicit retuning guideline according to the user's preference for performance or robustness. Simulation and laboratory water tank experiment validate the tuning efficacy and a coal mill temperature control test depicts a promising prospective of the proposed method in process control practice.
PDF
