Time-varying State Delays Research Articles

Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay

The output-feedback stabilisation problem is solved for discrete-time systems with time-varying delay in the state. A stability condition is first proposed, which is dependent on the minimum and maximum delay bounds. Based on this easily verifiable stability condition, the problems of stabilisation by static and dynamic output-feedback controllers are solved within the linear matrix inequality (LMI) framework. Since the obtained conditions for the existence of admissible controllers are not expressed as strict LMI conditions, the cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. In addition, the obtained results, including stability analysis, static output-feedback stabilisation and dynamic output-feedback stabilisation are further extended to discrete time-delay systems with norm-bounded uncertain parameters. Numerical examples are also presented to illustrate the applicability of the developed results.

Observability of Singularly Perturbed Linear Time-Dependent Differential Systems with Small Delay

A singularly perturbed linear time-dependent differential system with multiple point and distributed time-delays in state variables is considered. Values of the delays are of order of a small positive parameter multiplying a part of derivatives in the system. Two much simpler systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. These systems are in separate time scales, and they do not contain the small parameter any more. Connections between properties of observability of these systems and such a property of the original system itself, valid for all sufficiently small values of the parameter of singular perturbations, are established. These results are obtained for both, standard and nonstandard, types of the original system, and for two, Euclidean space and state-space, types of the observability.

A Balanced Model Reduction for Fuzzy Systems with Time Varying Delay

This paper deals with a balanced model reduction for T-S(Takagi-Sugeno) fuzzy systems with time varying state delay. We define a generalized controllability gramian and a generalized observability gramian for a stable T-S fuzzy delayed systems. We obtain a balanced state space realization using the generalized controllability and observability gramian and obtain a reduced model by truncating states from the balanced state space realization. We also present an upper bound of the approximation error. The generalized controllability gramian and observability gramian can be computed from solutions of linear matrix inequalities. We demonstrate the efficacy of the suggested method by illustrating a numerical example.

Robust L/sub 2/-L∞ filtering for uncertain systems with multiple time-varying state delays

This paper is concerned with the robust L/sub 2/-L/sub /spl infin// filtering problem for uncertain systems with multiple time-varying state delays. The uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed energy-to-peak noise-attenuation level for all admissible uncertainties and time delays. The admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Both delay-independent and dependent approaches are presented, with an example illustrating the validity of the proposed designs.

Robust H control of uncertain systems with time-varying state and control input delays

Robust H control of uncertain systems with time-varying state and control input delays

H∞ control via output feedback for linear systems with time-varying delays in state and control input

In this paper, an observer-based H ∞ controller for systems with time-varying delays in state and control input is proposed. Using the solution of proposed modified algebraic Riccati equation, we can construct a controller which depends on the maximum value of the time derivative of time-varying delay and guarantees a prescribed H ∞ norm bound of the closed-loop transfer matrix from the disturbance to the controlled output. A given example illustrates the availability of the proposed design method.

Genetic fuzzy control for time-varying delayed uncertain systems with a robust stability safeguard

This paper proposes a new delay-independent stability criterion for uncertain systems with state time-varying delay. Then, a robust state feedback control law based on it is constructed via sequential quadratic programming method to stabilize uncertain systems. Add a proposed FLC with a small number of rules and membership functions to the above-mentioned robust state feedback control law such that not only closed-loop uncertain systems with time-varying delay are robust stable but also output performance approaches desired one. An example given illustrates the availability of the proposed design method.

Robust Output-Feedback Control for Linear Continuous Uncertain State Delayed Systems with Unknown Time Delay

The state-delayed time often is unknown and independent of other variables in most real physical systems. In this paper, a new stability criterion for uncertain systems with a state time-varying delay is proposed. Then, a robust observer-based control law based on this criterion is constructed via the sequential quadratic programming method. We also develop a separation property so that the state feedback control law and observer can be independently designed and maintain closed-loop system stability. An example illustrates the availability of the proposed design method.

Robust control of delay systems: a sliding mode control design via LMI

This paper considers the sliding mode control of uncertain systems with single or multiple, constant or time-varying state-delays, submitted to additive perturbations. The sliding surface is designed so to maximize the calculable set of admissible delays. The conditions for the existence of the sliding regime are studied by using Lyapunov–Krasovskii functionals and Lyapunov-Razumikhin functions. LMIs are used for the optimization procedure. Two examples illustrate the proposed method.

Robust H∞ filter design for uncertain linear systems with multiple time-varying state delays

The problem of robust H/spl infin/ filtering for continuous-time uncertain linear systems with multiple time-varying delays in the state variables is investigated. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. The aim is to design a stable linear filter assuring asymptotic stability and a prescribed H/spl infin/ performance level for the filtering error system, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities, which can be efficiently solved by means of powerful convex programming tools with global convergence assured. An example illustrates the proposed methodology.

Robust mixed H 2 /H ∞ control of time-varying delay systems

This paper describes the mixed H 2 /H X controller design method of linear systems with time-varying delays in both state and control input. More specifically, the proposed mixed H 2 /H X controller minimizes the H 2 performance measure when satisfying a prescribed H X norm bound on the closed loop system. The sufficient conditions for the existence of controller, the mixed H 2 /H X controller design method and the upper bound of performance measure are presented using the linear matrix inequality (LMI) technique. Also, all solutions including controller gain and the upper bound of performance measure are obtained simultaneously. Furthermore, the proposed controller design method can be easily extended into the problem of robust mixed H 2 /H X controller design method for parameter uncertain systems with time-varying delays in both state and control input.

Design of adaptive variable structure controllers for perturbed time-varying state delay systems

The problem of stabilizing a class of perturbed linear dynamic systems with time-varying state delay is investigated in this paper. By applying the Lyapunov stability theorem, we develop a delay-independent adaptive variable structure controller to drive the states of system to zero. Based on the variable structure control (VSC) technique, the proposed controller can drive the system into a pre-specified sliding hyperplane to obtain the desired dynamic performance. Once the dynamics of system reach the sliding plane, the proposed controlled system is insensitive to perturbations. The use of adaptive technique is to overcome the unknown upper bound of perturbations so that the reaching condition (or sliding condition) can be satisfied. Furthermore, the globally asymptotic stability is guaranteed for the proposed control scheme under certain conditions. Finally, an example is given to illustrate the feasibility of the proposed control methodology.

Output feedback robust H/sup /spl infin/#x221E;/ control of uncertain fuzzy dynamic systems with time-varying delay

This paper presents an output feedback robust H/sup /spl infin// control problem for a class of uncertain fuzzy dynamic systems with time-varying delayed state. The Takagi-Sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single quadratic Lyapunov function, the globally exponential stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust H/sup /spl infin// controllers are given in terms of matrix inequalities. Constructive algorithm for design of robust H/sup /spl infin// controller is also developed. The resulting controller is nonlinear and automatically tuned based on fuzzy operation.

状態むだ時間非線形システムの有限極配置

In this paper single input nonlinear systems with non-commensurate time-delays in state variables are considered. The objective is to design a coordinates transformation and a feedback which yield a finite dimensional linear controllable closed-loop system in a new coordinates, whose spectrum is located at an arbitrarily preassigned set of n points in the complex plane. An algebraic design procedure for this problem is proposed here. The proposed method is related to the exact linearization technique for systems with a finite dimension, and recognized as the extension of the finite spectrum assignment of linear retarded systems. Effectiveness of the method is tested by illustrative examples.

Formula omitted] control of discrete-time linear systems with time-varying delays in state

This paper deals with the H ∞ control problems for discrete-time linear systems with time-varying delays in state. In this paper, the H ∞ control law is assumed to be a memoryless state feedback and the size of time-varying delays considered is upper-bounded. The solution of the H ∞ control problem for discrete-time linear systems with time-varying delays in state can be obtained by solving an H ∞ control problem for auxiliary discrete-time linear systems with no time delays.

Adaptive robust control of uncertain systems with time-varying state delay

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time-varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time-delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.

Finite spectrum assignment for nonlinear systems with non-commensurate delays

In this paper single input nonlinear systems with non-commensurate timedelays in state variables are considered. The objective is to design a coordinates transformation and a feedback which yield a finite dimensional linear controllable closed-loop system in a new coordinates, whose spectrum is located at an arbitrarily preassigned set of n points in the complex plane. An algebraic design procedure for this problem is proposed here. The proposed method is related to the exact linearization technique for systems with a finite dimension, and recognized as the extension of the finite spectrum assignment of linear retarded systems.

Robust stability and stabilization of linear delayed systems with structured uncertainty

This paper shows criteria for robust stability and stabilization of linear state-delayed systems with structured uncertainty. We consider the structured uncertainty composed of repeated scalar-block and full-block forms and a time-varying state delay. Delay-dependent methods for robust stability and stabilization are provided in terms of linear matrix inequalities. For linear systems with structured uncertainty and a time-varying state delay, the proposed methods give less conservative results than those obtained via the methods accounting for only norm-boundedness of the uncertainty.

Robust H∞ controller design for time-varying uncertain linear systems with time-varying state and control delays

The robust H∞ control problem for time-varying uncertain linear systems with time-varying state, and control delays is considered. Based on the Riccati equation approach, we design a robust H∞ linear time-invariant state feedback control law, which stabilizes the system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. A sufficient condition for the existence of the. robust H∞ controller is derived and two synthesis methods are presented for a robust H∞ control law to uncertain time-delay systems. One is to construct a robust H∞ control law by an equivalent linear time-invariant structural description for the sufficient condition and the control law can be obtained by solving an algebraic Riccati equation (ARE). The other method is to transform the sufficient condition into a linear matrix inequality (LMF) problem and the control law can be obtained by solving the LMI. A numerical example is presented to illustrate the obtained results.

H∞-output feedback controller design for linear systems with time-varying delayed state

This paper considers the H/spl infin/-controller design problem for linear systems with time-varying delays in states. The authors obtain sufficient conditions for the existence of H/spl infin/ controllers in terms of three linear matrix inequalities (LMIs). These sufficient conditions are dependent on the maximum value of the time derivative of time-varying delay. Furthermore, they briefly explain how to construct such controllers from the positive-definite solutions of their LMIs and give an example.