Observer-based passive control for linear system with time-varying delays in state and control input

This paper deals with the robust passivity synthesis problem for a class of uncertain linear systems with time-varying delay in state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all matrices of the model. The problem aims at designing an observer-based dynamic output-feedback controller that robustly stabilizes the uncertain systems and achieves the strict passivity of closed-loop systems for all admissible uncertainties. By converting the problem at hand into a class of strictly passive control problem for a parameterized system, the explicit solution is established and expressed in terms of a linear matrix inequality. A numerical example is provided to demonstrate the validity of the proposed approach.

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

A robust controller is developed for uncertain, second-order nonlinear\nsystems subject to simultaneous unknown, time-varying state delays and known,\ntime-varying input delays in addition to additive, sufficiently smooth\ndisturbances. An integral term composed of previous control values facilitates\na delay-free open-loop error system and the development of the feedback control\nstructure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals\nguarantees uniformly ultimately bounded tracking under the assumption that the\ndelays are bounded and slowly varying.\n

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario. Copyright © 2016 John Wiley & Sons, Ltd.

A novel power and rate control system model for wireless communication networks is presented, which includes uncertainties, input constraints, and time-varying delays in both state and control input. A robust delay-dependent model predictive power and rate control method is proposed, and the state feedback control law is obtained by solving an optimization problem that is derived by using linear matrix inequality (LMI) techniques. Simulation results are given to illustrate the effectiveness of the proposed method.

The dissipative analysis and control synthesis for uncertain singular systems with interval time-varying state and input delays are investigated in this paper. The parametric uncertainty in this paper is assumed to be norm bounded. A sufficient condition, in the form of linear matrix inequality (LMI) with nonlinear constraints, on the existence of robust dissipative controller is established based on the Lyapunov stability theory. In order to solve the nonlinear problem, Cone Complementarity Linearization (CCL) is offered.

This paper establishes a framework for stability analysis and memoryless state-feedback control synthesis of linear discrete-time systems with time varying state delay. The underlying idea is converting the considered system into an equivalent constrained switched system, leading to sufficient and necessary condition for stability analysis. Based on this switched system modeling, available information about the time-varying delay such as known bounds of variation rate can be incorporated into the analysis in a natural way. Moreover, sufficient conditions for memoryless state-feedback control design are obtained in a similar style. The analysis and synthesis conditions are given in terms of solvability of a set of linear matrix inequalities (LMIs). Numerical examples are included for illustration.

The output feedback stabilization of polytopic-type uncertain discrete systems with interval-like time-varying state and input delays is studied. Based on a new bounding inequality technique, combining a parameter-dependent Lyapunov functional, a stability criterion is firstly presented in terms of a set of simple convex feasibility tests. Then, the output feedback stabilization conditions are formulated in the form of non-convex matrix inequalities, of which a feasible solution can be obtained by solving an LMI-based minimization problem. The newly proposed inequality lies in the partitioning idea of the varying interval and shows its more tightness over some existing bounding techniques. No free weighting matrix is involved. Two illustrative examples are finally given to verify the advantage and effectiveness of the proposed method.

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

Autonomous systems often use feedback from an imaging system for guidance, navigation, and control. Such feedback requires an image processing method that yields an inherent delay in state measurements. For some camera-to-hand applications, the image-based sensing and control computations may be computed by a more capable processor and then be transmitted to a sensorless vehicle, resulting in a delay in control execution. To account for these delays, an approach is developed in this paper that applies a transformation, to separate the image coordinates into spatial and time domain components. This transformation, along with a novel integral error system, allows for the development of a robust controller that compensates for uncertain time-varying state delays and known time-varying input delays for nonlinear image dynamics. A Lyapunov-based stability analysis is used to prove that the developed controller enables a sensorless autonomous vehicle to yield uniformly ultimately bounded (UUB) tracking of a desired image trajectory.

This paper addressed the problem of delay dependent stabilization for linear parameter-varying systems with time-varying state and input delays. A new delay-dependent criterion is developed by constructing the reduction method and combining with the parameter-dependent Lyapunov approach. Sufficient conditions are presented to design gain-scheduled controller to stabilize the closed-loop systems from past input information in terms of parameterized linear matrix inequalities. The effectiveness is shown via an numerical example.

This paper proposes a discrete-time sliding mode control (DT-SMC) algorithm for uncertain linear systems with time-varying delay on the state. The parameter uncertainties and the external disturbances are assumed to be unknown but norm-bounded. The sliding mode existence depends on that of the stable linear sliding surface, which is ensured by a sufficient condition that depends on the delay bounds and is derived using LMI. A numerical example as well as an application to the Two-Area Four-Machine power system has been presented to illustrate and confirm the usefulness and the effectiveness of the proposed control strategy.

In this paper, a dynamic decoupling approach is proposed to improve the robust Takagi-Sugeno (T-S) fuzzy model-based control to cope with system uncertainty, input actuator nonlinearity, and input time delay. First, the basic dynamic decoupling concept is introduced by involving virtual input dynamics, such that the system uncertainty and control input are decoupled in each fuzzy rule. This leads to simplified linear matrix inequality (LMI) conditions. Next, the dynamic decoupling approach is extended to controlling uncertain systems with input actuator nonlinearity (e.g., saturation, quantization, dead-zone, etc.) or time-varying input delay. Due to the decoupling between uncertainty, actuator nonlinearity, and input delay, more relaxed stability conditions are obtained for the asymptotic stability and H ∞ control performance. Furthermore, the limit on the initial condition is removed when considering input saturation. Larger and faster time-varying state and input delays are allowed under fewer LMIs. Finally, to show the advantages of the developed control method, numerical simulations are carried out on an inverted pendulum (subject to either the saturation, quantization, or delay input), a delay mass-spring-damper system, and a delay truck-trailer system.

Sufficient conditions are developed for the relative controllability of nonlinear neutral systems with time-varying multiple delays in both state and control. The results are obtained by using Schauder's fixed-point theorem Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 559-564

Mainly due to these advantages variable structure control theory has found applications in various kinds of plants (see, e.g. [86], [175], [33], [85]. Other SMC schemes are proposed for linear systems with state delay [161], [104], [100], and system with input delay [147]. Their methods have the same benefits, but cannot be applied to systems with both state and input delay. In a recent paper [63], the authors propose the design methods of a SMC for systems with both input and state delay. However, the results of [63] involve the tuning and factorizing of a symmetric positive-definite matrix. Because no tuning procedure for such matrix is available, this makes the use of these methods somehow difficult, especially when one wants to find the largest possible bound for the time delay which ensures stabilization.