Time-varying State Delays Research Articles

New Stability Criteria for Linear Systems with Interval Time-varying State Delays

In the present paper, the problem of stability analysis for linear systems with interval time-varying delays is considered. By introducing a new Lyapunov-Krasovskii functional, new stability criteria are derived in terms of linear matrix inequalities (LMIs). Two numerical examples are given to show the superiority of the proposed method.

Neural observer-based adaptive compensation control for nonlinear time-varying delays systems with input constraints

This paper describes a neural network state observer-based adaptive saturation compensation control for a class of time-varying delayed nonlinear systems with input constraints. An advantage of the presented study lies in that the state estimation problem for a class of uncertain systems with time-varying state delays and input saturation nonlinearities is handled by using the NNs learning process strategy, novel type Lyapunov–Krasovskii functional and the adaptive memoryless neural network observer. Furthermore, by utilizing the property of the function tan h 2( ϑ/ ϵ)/ ϑ, NNs compensation technique and backstepping method, an adaptive output feedback controller is constructed which not only efficiently avoids the problem of controller singularity and input saturation, but also can achieve the output tracking. And the proposed approach is obtained free of any restrictive assumptions on the delayed states and Lispchitz condition for the unknown nonlinear functions. The semiglobal uniform ultimate boundedness of all signals of the closed-loop systems and the convergence of tracking error to a small neighborhood are all rigorously proven based on the NN-basis function property, Lyapunov method and sliding model theory. Finally, two examples are simulated to confirm the effectiveness and applicability of the proposed approach.

An output-feedback adaptive actuator failure compensation controller for systems with unknown state delays

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.

Improved delay-range-dependent robust stability criteria for a class of Lur’e systems with sector-bounded nonlinearity

In this paper, the problem of delay-dependent stability of a class of uncertain Lur’e systems of neutral type with interval time-varying state delay and sector-bounded nonlinearity has been considered based on Lyapunov–Krasovskii functional approach. By constructing a candidate Lyapunov–Krasovskii (LK) functional, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMIs). The reduction in conservatism of the proposed stability criteria over recently reported results is attributed to the candidate LK functional used in the delay-dependent stability analysis, and to the tighter bounding of the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability condition in convex LMI framework, and is solved non-conservatively at boundary conditions using standard numerical packages. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems. A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input. An adaptive asymptotically stabilizing controller, which can guarantee the stability of the closed-loop system and the convergence of the original system state, is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) and nonlinear adaptive techniques. Some numerical examples are presented to demonstrate the effectiveness of the derived controller.

Stability Analysis for Discrete-Time Stochastic Neural Networks with Mixed Time Delays via Delay-Paritioning

This paper revisits the problem of stability analysis for discrete-time stochastic neural networks (DSNNs) with mixed time-varying delays in the state. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time varying norm bounded parameter uncertainties. A new delay-dependent stability criterion is presented by constructing a novel Lyapunov-Krasovskii functional and utilizing the delay partitioning idea and free-weighting matrix approach, Which is less conservative than the existing ones. This criterion can be developed in the frame of convex optimization problems and then solved via standard numerical software. These conditions are formulated in the forms of linear matrix inequalities, which feasibility can be easily checked by using Matlab LMI Toolbox.

Necessary and sufficient asymptotic stability criterion for 2-D positive systems with time-varying state delays described by Roesser model

This study addresses the stability problem of two-dimensional (2-D) positive systems described by Roesser model and involving delays in the states. The delays are time varying and bounded. A necessary and sufficient stability condition is established for such systems. It is shown that a 2-D positive system with time-varying delays is asymptotically stable for any bounded delays if and only if the corresponding constantly delayed system is asymptotically stable, or equivalently, if and only if the sum of the system matrices is a Schur matrix. An example illustrates the theoretical result.

Multi-Agent Consensus with a Time-Varying Reference State and Time-Varying Delays

This paper is devoted to the study of consensus problem of multi-agent systems with a time-varying reference state in directed networks with both switching topology and time-delay. Stability analysis is performed based on a proposed Lyapunov–Krasovskii function. Sufficient conditions based on linear matrix inequalities (LMIs) are given to guarantee that multi-agent consensus on a time-varying reference state can be achieved under arbitrary switching of the network topology even if the network communication is affected by time-delay. These consensus algorithms are also extended to consensus formation among the agents. Finally, simulation example is given to validate our theoretical results.

Robust stabilization of polytopic discrete-time systems with time-varying state delay: A convex approach

Abstract Convex conditions, expressed as linear matrix inequalities (LMIs), for stability analysis and robust design of uncertain discrete-time systems with time-varying delay are presented in this paper. Delay-dependent and delay-independent convex conditions are given. This paper is particularly devoted to the synthesis case where convex conditions are proposed to consider maximum allowed delay interval. It is also presented some relaxed LMIs that yield less conservative conditions at the expense of increasing the computational burden. Extensions to cope with decentralized control and output feedback control are discussed. Numerical examples, including real world motivated models, are presented to illustrate the effectiveness of the proposed approach.

Delay-dependent stability analysis for discrete-time systems with time varying state delay

The stability of discrete systems with time-varying delay is considered. Some sufficient delaydependent stability conditions are derived using an appropriate model transformation of the original system. The criteria are presented in the form of LMI, which are dependent on the minimum and maximum delay bounds. It is shown that the stability criteria are approximately the same conservative as the existing ones, but have much simpler mathematical form. The numerical example is presented to illustrate the applicability of the developed results.

Decentralized Adaptive Robust Control of Uncertain Large Scale Systems Including Time–Varying State Delays in the Nonlinear Interconnections

AbstractThe problem of decentralized adaptive robust stabilization is considered for a class of uncertain large scale time–delay systems with nonlinear interconnection terms. It is assumed that the upper bounds of the uncertainties and the interconnection terms are unknown, and that the time–varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear interconnection terms, which can also include time–varying delays, are bounded in any nonnegative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain large scale time–delay nonlinear systems, a new method is presented whereby a class of decentralized local adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain large scale time–delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Copyright ©2011 IFAC

Output-Feedback MRAC with Reference Model Tolerance of Nonlinearly Perturbed Delayed Plants

AbstractA novel approach within the conventional MRAC framework for solving the problem of robust adaptive output tracking for a class of uncertain nonlinear dynamical systems with unknown time-varying state delays is proposed. A MRAC problem formulation in addition to the traditional asymptotic zero error tracking specification makes the problem statement contain an additional explicit requirement, namely the tracking objective is described by a set of admissible reference trajectories which is called a performance tube. As the design parameter which specifies the size of the performance tube, we select the reference model input signal than can be changed within specified bounds. An additional optimization task is formulated to find the best trajectory with a cost function that penalizes the deviation of the control signal from a given signal.

Continuous Decentralized MRAC with Sliding Mode of Nonlinear Delayed Dynamic Systems

AbstractIn this contribution, we develop continuous totally decentralized state-feedback adaptive controllers with sliding mode for a class of large-scale interconnected systems with nonlinear interconnections with unknown time-varying state delays. The novel contribution of this paper is that asymptotically exact tracking within the framework of totally decentralized direct continuous adaptive control is possible also for the class of nonlinear plants considered here.

Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays

Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays

Sliding Mode Control for Linear Systems with Time-Varying Input and State Delays

This paper deals with a sliding mode control for linear systems with input and state time-varying delays. Two different time delays are considered for the sliding mode control of a continuous linear system. Delay-dependent sufficient conditions are given for the existence of sliding manifolds in terms of linear matrix inequalities. A reaching motion controller is also proposed for such systems by means of both reaching law and inequality approach. An inverted pendulum system is utilized to illustrate the effectiveness of the developed techniques.

Sliding-mode control of uncertain systems in the presence of unmatched disturbances with applications

This article considers the development of constructive sliding-mode control strategies based on measured output information only for linear, time-delay systems with bounded disturbances that are not necessarily matched. The novel feature of the method is that linear matrix inequalities are derived to compute solutions to both the existence problem and the finite time reachability problem that minimise the ultimate bound of the reduced-order sliding-mode dynamics in the presence of state time-varying delay and unmatched disturbances. The methodology provides guarantees on the level of closed-loop performance that will be achieved by uncertain systems which experience delay. The methodology is also shown to facilitate sliding-mode controller design for systems with polytopic uncertainties, where the uncertainty may appear in all blocks of the system matrices. A time-delay model with polytopic uncertainties from the literature provides a tutorial example of the proposed method. A case study involving the practical application of the design methodology in the area of autonomous vehicle control is also presented.

Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays

Abstract In this paper, an improved mean-square exponential stability condition and delayed-state-feedback controller for stochastic Markovian jump systems with mode-dependent time-varying state delays are obtained. First, by constructing a modified Lyapunov-Krasovskii functional, a mean-square exponential stability condition for the above systems is presented in terms of linear matrix inequalities (LMIs). Here, the decay rate can be a finite positive constant in a range and the derivative of time-varying delays is only required to have an upper bound which is not required to be less than 1. Then, based on the proposed stability condition, a delayed-state-feedback controller is designed. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.

Adaptive stabilisation for a class of non-linear state time-varying delay systems with unknown time-delay bound

In this study, the authors address the problem of adaptive backstepping control for a class of single-input and single-output (SISO) non-linear time-delay systems in triangular structure. Both the parameters of the system to be controlled and the upper bounds of the time delays and their derivatives are assumed to be unknown. A direct adaptive controller for this class of uncertain non-linear systems is proposed. The assumption on delay-related non-linearities is further relaxed. An appropriate Lyapunov–Krasovskii functional is constructed, and the backstepping technique is used. It is shown that all the closed-loop signals are bounded, while the plant states converge to zero asymptotically. A simulation example is provided to demonstrate the design procedure and performance of the proposed method.

Approximation-Based Adaptive Tracking Control of Pure-Feedback Nonlinear Systems With Multiple Unknown Time-Varying Delays

This paper presents adaptive neural tracking control for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays. To overcome the design difficulty from non-affine structure of pure-feedback system, mean value theorem is exploited to deduce affine appearance of state variables x(i) as virtual controls α(i), and of the actual control u. The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state. The novel Lyapunov-Krasovskii functionals are employed to compensate for the unknown functions of current delayed state, which is effectively free from any restriction on unknown time-delay functions and overcomes the circular construction of controller caused by the neural approximation of a function of u and [Formula: see text] . Novel continuous functions are introduced to overcome the design difficulty deduced from the use of one adaptive parameter. To achieve uniformly ultimate boundedness of all the signals in the closed-loop system and tracking performance, control gains are effectively modified as a dynamic form with a class of even function, which makes stability analysis be carried out at the present of multiple time-varying delays. Simulation studies are provided to demonstrate the effectiveness of the proposed scheme.

Adaptive fuzzy controller for multivariable nonlinear state time-varying delay systems subject to input nonlinearities

In this paper, an adaptive fuzzy variable-structure controller is investigated for a class of uncertain multi-input multi-output (MIMO) nonlinear time-delay systems with both sector nonlinearities and dead-zones. A decomposition property of the control-gain matrix is fully exploited in the controller design and the stability analysis. The unknown time-varying delay uncertainties are compensated for using an appropriate Lyapunov–Krasovskii functional. The boundedness of all signals of the closed-loop system as well as the exponential convergence of the underlying tracking errors to an adjustable region are established. The effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results.