Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Delay-dependent robust control for uncertain discrete singular systems with time-varying delay

The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.

Improved Results on Robust H_∞ Control of Uncertain Discrete-time Systems with Time-varying Delay

In this paper, the robust H∞ control problem for uncertain discrete-time systems with time-varying state delay is con- sidered. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional, a new less conservative sufficient condition for the existence of a robust H∞ controller is obtained. Moreover, the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem. Finally, several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Designing Discrete Predictor-Based Controllers for Networked Control Systems with Time-varying Delays:Application to A Visual Servo Inverted Pendulum System

A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant delay,which can be potentially applied to vision-based control systems.The control scheme is composed of a state prediction and a discrete predictor-based controller.The state prediction is used to compensate for the effect of the sensor-to-controller delay,and the system can be stabilized by the discrete predictor-based controller.Moreover,it is shown that the control scheme is also robust with respect to slight message rejections.Finally,the main theoretical results are illustrated by simulation results and experimental results based on a networked visual servo inverted pendulum system.

Exponential stability for networked control systems based on the model of nonlinear discrete-time system with time-varying delay

An uncertain nonlinear discrete-time system model with time-varying input delays for networked control systems (NCSs) is presented. The problem of exponential stability for the system is considered and some new criteria of exponential stability are obtained based on norm inequality methods. A numerical example is given todemonstrate that those criteria are useful to analyzing the stability of nonlinear NCSs.

Stabilization of a class of nonlinear discrete time systems with time varying delay

The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.

Delay-Dependent Robust Passive Control for Uncertain Discrete-Time Systems with Time Delays

This paper considers the problem of robust passive control for uncertain discrete systems with time-varying delays. We pay attention to designing a state feedback controller which guarantees the passivity of the closed-loop system for all admissible uncertainties. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented and the explicit expression of the desired state feedback controller is given.

Real-Valued Discrete Gabor Transform of Linear Time-Varying Systems: Exact Representation and Approximation

An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.

Consensus of high-order dynamic multi-agent systems with switching topology and time-varying delays

This paper studies the consensus problems for a group of agents with switching topology and time-varying communication delays, where the dynamics of agents is modeled as a high-order integrator. A linear distributed consensus protocol is proposed, which only depends on the agent＇s own information and its neighbors＇ partial information. By introducing a decomposition of the state vector and performing a state space transformation, the closed-loop dynamics of the multi-agent system is converted into two decoupled subsystems. Based on the decoupled subsystems, some sufficient conditions for the convergence to consensus are established, which provide the upper bounds on the admissible communication delays. Also, the explicit expression of the consensus state is derived. Moreover, the results on the consensus seeking of the group of high-order agents have been extended to a network of agents with dynamics modeled as a completely controllable linear time-invariant system. It is proved that the convergence to consensus of this network is equivalent to that of the group of high-order agents. Finally, some numerical examples are given to demonstrate the effectiveness of the main results.

Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay.The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval.The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer.The second contribution of this paper is to introduce a novel LyapunovKrasovskii functional,which includes a cubic polynomial on a time-varying delay,in stability analysis of time-delay systems.Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities,two stability criteria are derived for two cases of the time-varying delay.A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control （AILC） scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality （LMI） method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative （PID） feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function （CEF）, we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

Adaptive Variable Structure Control of MIMO Nonlinear Systems with Time-varying Delays and Unknown Dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output （MIMO） nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncer- tainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.

Robust Leader-Following Output Regulation of Uncertain Multi-Agent Systems With Time-Varying Delay

In this paper, the robust analysis and design of leader-following output regulation for multi-agent systems described by general linear models is given in presence of timevarying delay and model uncertainty. To this aim, a new regulation protocol for the closed-loop multi-agent system under a directed graph is proposed. An important specification of the proposed protocol is to guarantee the leader-following output regulation for uncertain multi-agent systems with both stable and unstable agents. Since many signals can be approximated by a combination of the stationary and ramp signals, the presented results work for adequate variety of the leaders. The analysis and design conditions are presented in terms of certain matrix inequalities. The method proposed can be used for both stationary and ramp leaders. Simulation results are presented to show the effectiveness of the proposed method.

Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems

The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.

Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.

Fault detection and optimization for networked control systems with uncertain time-varying delay

The observer-based robust fault detection filter design and optimization for networked control systems （NOSs） with uncer- tain time-varying delays are addressed. The NCSs with uncertain time-varying delays are modeled as parameter-uncertain systems by the matrix theory. Based on the model, an observer-based residual generator is constructed and the sufficient condition for the existence of the desired fault detection filter is derived in terms of the linear matrix inequality. Furthermore, a time domain opti- mization approach is proposed to improve the performance of the fault detection system. To prevent the false alarms, a new thresh- old function is established, and the solution of the optimization problem is given by using the singular value decomposition （SVD） of the matrix. A numerical example is provided to illustrate the effectiveness of the proposed approach.

Delay-dependent robust stability and H_∞ analysis of stochastic systems with time-varying delay

This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He＇s technique, and a stochastic Lyapunov-Krasovskii functional, new delay-dependent criteria in terms of linear matrix inequalities are derived for the the robust stochastic stability and the H∞ disturbance attenuation. Three numerical examples axe given. The results show that the proposed method is efficient and much less conservative than the existing results in the literature.

Optimal guaranteed cost control for fuzzy descriptor systems with time-varying delay

Based on the delay-independent rule, the problem of optimal guaranteed cost control for a class of Takagi-Sugeno （T-S） fuzzy descriptor systems with time-varying delay is studied. A linear quadratic cost function is considered as the performance index of the closed-loop system. Sufficient conditions for the existence of guaranteed cost controllers via state feedback are given in terms of linear matrix inequalities （LMIs）, and the design of an optimal guaranteed cost controller can be reduced to a convex optimization problem. It is shown that the designed controller not only guarantees the asymptotic stability of the closed-loop fuzzy descriptor delay system, but also provides an optimized upper bound of the guaranteed cost. At last, a numerical example is given to illustrate the effectiveness of the proposed method and the perfect performance of the optimal guaranteed cost controller.

Stability criteria for linear systems with multiple time-varying delays

New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. Keywords Stability - Delay-independent criteria - Delay-dependent criteria - Linear time-delay systems - Multiple time-varying delays This work was supported by NSFC Key-Project (No. 60334010) and Guangdong Province Natural Science Foundation of China (No. 31406).

A New Robust Stabilization Analysis Result for Uncertain Systems with Time-Varying Delay

The robust stabilization problem for uncertain systems with time-varying delay has been discussed. A new sufficient criterion is obtained to guarantee the closed-loop system robust stabilizable. The controller gain matrix is included in a Hamiltonian matrix. The Hamiltonian matrix can be constructed by the boundedness of the uncertainties. Some examples are given to illustrate the feasibility of the criterion.