Simple stabilizability criteria and memoryless state feedback control design for time-delay systems with time-varying perturbations

In this paper, the problems of stabilization for interval type-2 fuzzy systems with time-varying delay and parameter uncertainties are investigated. The objective is to design an interval type-2 fuzzy controller such that the closed-loop control system is asymptotically stable. The conditions for the existence of such a controller are delay dependent and membership function dependent in terms of linear matrix inequalities (LMIs). Based on a basic lemma, we formulate and solve the problem with more flexibility due to imperfect premise matching that the number of rules and premise membership functions are not necessary the same between the interval type-2 fuzzy model and interval type-2 fuzzy controller. A systematic approach making use of the information embedded in the lower and upper membership functions is employed to facilitate the stability analysis. A numerical example indicates the effectiveness of the derived results.

In this paper, the pinning synchronization of coupled memristive recurrent neural networks (MNNs) with mixed time-varying delays and perturbations is investigated. Precisely, the considered coupled MNNs include the non-delay, discrete time-varying delays, distributed time delays, impulsive perturbations and stochastic perturbations. Comparing with the existing results, the new and simple feedback controller and adaptive feedback controller are designed to achieve exponential synchronization with pinning schemes. Based on the suitable Lyapunov functional and the definition of pinning control, with the aid of inequality techniques and differential inclusions theory, some effective and novel sufficient conditions are obtained to guarantee the synchronization of our proposed model. Finally, numerical examples are given to illustrate the effectiveness and reasonable of our theoretical results.

The proportional-integral-derivative (PID) controller design for time-delay systems is a classical problem. We consider a general case where the three controller gains (k P , k I , and k D ) and the delay (τ) are all treated as free parameters. Our objective is to characterize the stability set in the parameter space of (k P ; k I ; k D ; τ). The problem is very involved due to the theoretical difficulties. In this paper, we introduce a MATLAB-based toolbox, called PID-Design-Delay toolbox. It is developed based on some recently-reported theoretical results, by which the problem can be systematically solved. The user is only required to input the necessary information via the graphical user interface (GUI) and then the stability analysis may be automatically fulfilled by the toolbox.

Time delays are inherent in modern motion-control and electric-drive loops due to sensing, filtering, sampling and computation, communication, and actuation scheduling. When such delays are only partially known, they can markedly reduce stability margins and narrow the admissible range of state-feedback gains, especially in high-bandwidth servo applications. This paper develops a design-oriented state-feedback framework for delay-affected plants based on the Manabe polynomial concept and the Coefficient Diagram Method (CDM). The plant is represented as a chain of integrators of order two to four with an effective input gain, and the feedback gain is synthesized for the nominal delay-free model by matching a standard Manabe/CDM characteristic polynomial using the classical CDM stability-index pattern. When an unmodeled input delay is present, the closed loop is governed by a delay-dependent characteristic equation. By introducing a normalized representation, the analysis yields explicit delay-stability limits that directly translate into a lower bound on the equivalent time constant used for tuning. The degradation of the phase margin and gain margin with increasing normalized delay is quantified as design charts, and a simple phase-margin-based inequality is proposed for selecting the tuning time constant, with gain-margin checks recommended as a verification step.

A new robust stability criterion is developed to guarantee the stability of the feedback systems subjected to noises and nonlinear time-varying plant perturbations. The main contribution of this paper is an extension of the results of robust stability for the class of feedback systems containing nonlinear time-varying plant perturbations to the class of systems with unstable plants and noises. The generally parameterized stabilizing controller, advanced by Youla et al., is combined with Schur function (class S) to synthesize the robust stabilizers of the feedback systems subjected to noises and nonlinear time-varying plant perturbations.

The study proposes a new simple output feedback adaptive tracking control scheme using neural network for a class of complicated modern agricultural mechanical systems that only the system output variables can be measured. The scheme avoids design state observer and Lipschiz assumption, SPR conditions are not required and few parameters in control laws and weights update laws need to be tuned. Only one RBF neural network is employed to approximate the lumped uncertain nonlinear function. The stability analysis of the closed-loop system is performing using a Lyapunov approach which shows that the output tracking error and all states in the closed-loop system are boundedness. The effectiveness of the proposed adaptive control scheme is demonstrated through the simulations.

The optimal model simplification technique which was originally proposed for the simplification of systems having simple delays in the numerator transfer functions has been extended to systems having several numerator delays such as quasirational and related systems. The design of simple feedback controllers for such systems has engaged the attention of researchers for sometime. In this work, it is shown that by using the internal model control method, the optimal simplified models can be used to parametrize simple feedback controllers for these systems. This procedure facilitates the deployment of a very effective and powerful controller design technique for quasirational and related systems.

This paper is concerned with the stability problems and robust analysis of a class of discrete-time interval systems with time-varying, infinite distributed delays and uncertainties. A novel delay-independent stability criterion based on Gronwall's inequalities in terms of Linear Matrix Inequalities (LMIs) is proposed. The example simulation is performed for the comparison of the proposed delay-independent stability criterion to those in the corresponding literatures, for purpose of testifying the effectiveness of the presented method. The simulation results show that the proposed algorithm has the advantage of less computational cost and larger delay upper.

The robust control problem for a class of uncertain time-delay systems is investigated. The systems include multiple time delays and uncertain nonlinear functions. To our best knowledge, no controller design method for the systems is reported in the literature except for sliding mode control (SMC). However, the sliding mode controller must use the delayed state of the system, so that the precise time delays have to be known, and also a large memory is needed for controller implementation. To overcome the shortcomings, we employ the backstepping method to design a memoryless state feedback controller. By constructing a novel Lyapunov-Krasovskii functional, we show that the resulting closed-loop system is asymptotically stable. Simulations are done to verify the effectiveness of the proposed method.

In this study, the exponential stability problem of impulsive system is investigated via sampled-data control in the presence of random time-varying delays and non-linear perturbations. In particular, the time delays are considered to be randomly time varying and they obey the Bernoulli distributions. The authors' main attention is focused on the design of a sampled-data controller to ensure an exponential stability for the closed-loop system. By extending the first- and second-order reciprocal convex approach, an efficient method called third-order reciprocal convex technique is used to manipulate the main results. Through the construction of a suitable Lyapunov–Krasovskii functional combined with input delay approach and Briat lemma, several delay-dependent sufficient conditions for the concerned system are derived in the form of linear matrix inequalities which can be readily solved by utilising the valid software packages. Some numerical examples are given to illustrate the effectiveness of the developed control technique.

This article concerns the stability and stabilisation of a linear system with both state and input delays. First, the combination of an augmented Lyapunov functional and the free-weighting-matrix technique yields a new delay-independent stability criterion that includes the widely used one as a special case. This criterion is then extended to a new delay-dependent stability criterion by employing an integral inequality. Based on that, a stabilisation approach to design a state feedback controller is presented that requires no parameter tuning, as is needed with some existing methods. Finally, numerical examples illustrate that the method is effective and is an improvement over existing ones.

This paper investigates the guaranteed cost control problem of uncertain non-linear systems with time-varying delays via the Takagi–Sugeno fuzzy model approach. Based on the Lyapunov–Krasovskii functional theory and the linear matrix inequality technique, a state feedback controller is proposed to stabilise the non-linear systems and minimise the guaranteed cost of the closed-loop systems. Both delay-dependent and delay-independent stability criteria are derived to guarantee the asymptotic stability of closed-loop systems. Furthermore, the supplementary requirement that the time-derivative of time-varying delays must be smaller than one is released for the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the validity of the results developed in this paper.

This paper addresses the problem of global robust fault accommodation tracking for a class of uncertain nonlinear systems with unknown powers and actuator faults. It is assumed that the powers of the concerned system are unknown time-varying functions, all system nonlinearities are unknown, and unknown actuator faults depend on the time-varying power of a control input. A fault accommodation state-feedback controller is explicitly constructed based on the nonlinear error transformation technique using time-varying performance functions. Global tracking with the preselected performance bounds is established in the presence of unknown time-varying powers and unexpected actuator faults. Different from the previous results dealing with the problem of unknown time-varying powers, the proposed tracking strategy does not require the knowledge of the bounds of the time-varying powers and the nonlinear bounding functions of system nonlinearities. An underactuated mechanical system is simulated to validate the effectiveness of the proposed theoretical approach.

In this note, we deal with the stability and stabilization problems for nonlinear quadratic discrete-time periodic systems. By using the quadratic Lyapunov function, and a so called periodic invariant set, delay-independent sufficient conditions for local stability and local stabilization for nonlinear quadratic discrete-time periodic systems are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.

This paper focuses on the issue of robustly exponential stability for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations. Some new sufficient conditions dependent on the delays are derived in terms of Lyapunov-Krasovskii functionals combined with free-weighting matrices. Two numerical examples are given to show the effectiveness of the proposed method.