Multiple Lyapunov-Krasovskii Research Articles

Adaptive Control of Semi-Autonomous Teleoperation System With Asymmetric Time-Varying Delays and Input Uncertainties.

This paper addresses the adaptive task-space bilateral teleoperation for heterogeneous master and slave robots to guarantee stability and tracking performance, where a novel semi-autonomous teleoperation framework is developed to ensure the safety and enhance the efficiency of the robot in remote site. The basic idea is to stabilize the tracking error in task space while enhancing the efficiency of complex teleoperation by using redundant slave robot with subtask control. To unify the study of the asymmetric time-varying delays, passive/nonpassive exogenous forces, dynamic parameter uncertainties and dead-zone input in the same framework, a novel switching technique-based adaptive control scheme is investigated, where a special switched error filter is developed. By replacing the derivatives of position errors with their filtered outputs in the coordinate torque design, and employing the multiple Lyapunov-Krasovskii functionals method, the complete closed-loop master (slave) system is proven to be state-independent input-to-output stable. It is shown that both the position tracking errors in task space and the adaptive parameter estimation errors remain bounded for any bounded exogenous forces. Moreover, by using the redundancy of the slave robot, the proposed teleoperation framework can autonomously achieve additional subtasks in the remote environment. Finally, the obtained results are demonstrated by the simulation.

Global exponential stability for switched memristive neural networks with time-varying delays

This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov–Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples.

Fault estimation for discrete-time switched nonlinear systems with discrete and distributed delays

Summary This paper is concerned with the fault estimation for a class of discrete-time switched nonlinear systems with mixed time delays. The fault existing in the system is assumed to be characterized by an external system, which incorporates the fault's prior knowledge to the considered systems. The fault estimator is designed by using the multiple Lyapunov–Krasovskii functional and average dwell-time approach. Sufficient conditions in the form of linear matrix inequalities (LMIs) are developed to ensure the resulting error system is exponentially stable with an optimized disturbance attenuation level. The gain matrices of the estimator can be easily determined by using the standard optimization toolboxes. Finally, numerical examples and simulation results with the help of real-time systems are given to illustrate the effectiveness and advantages of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.

Absolute exponential stability of switched nonlinear time-delay systems

This paper investigates absolute exponential stability of switched nonlinear time-delay systems in both continuous-time and discrete-time contexts. The nonlinearities of the systems satisfy a certain sector condition. First, an improved Lyapunov–Krasovskii functional of switched nonlinear time-delay systems in the continuous-time form is constructed. By using the multiple Lyapunov–Krasovskii functionals and average dwell time switching approaches, two less conservative sufficient conditions for the absolute exponential stability of the systems with single/multiple delays are established, respectively. Then, the obtained results are extended to discrete-time systems. All proposed conditions are described via linear programming. By some comparisons, it is shown that the results in the paper are less conservative than those in the literature. Finally, two examples are given to show the effectiveness of the theoretical findings.

Actuator fault-tolerant robust control of an uncertain networked control system with random time delays

In this paper, a novel robust fault-tolerant control scheme of networked flight control system against actuator faults with consideration of both norm-bounded uncertainties and time delays is proposed. Different from other research results on actuator fault-tolerant control methods, a complete fault model of actuators with partial failure is developed to represent the type and degree of actuator faults in an integrated parameterised way. Moreover, both of the time delays that are induced by avionic-bus and system uncertainties are considered to be described as mathematic parameters in complete fault model. By employing multiple parameter-dependent Lyapunov-Krasovskii functions, sufficient stability conditions of uncertain networked flight control systems with actuator faults are derived, and robust fault mode depended controllers are obtained in terms of linear matrix inequalities (LMIs), which is capable of accommodating uncertainties in the presence of actuator faults. Finally, examples are provided to illustrate the effectiveness of the proposed method.

Input-to-state stability and integral input-to-state stability for impulsive switched systems with time-delay under asynchronous switching

This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of impulsive switched systems with time-delay under asynchronous switching, using the method of multiple Lyapunov–Krasovskii functionals. The asynchronous switching means that the switchings between the candidate controllers and system modes are not synchronous due to the switching delay. It is shown that, even if all the subsystems governing the continuous dynamics, in the absence of impulses, are not ISS/iISS, impulses can successfully stabilize the system in the ISS/iISS sense with the matched controller if the length of the impulsive interval is large enough. Conversely, when the delayed continuous dynamics are ISS/iISS but the discrete dynamics governing the impulses are not, the ISS/iISS property of the hybrid system can be retained with the matched controller if the impulsive interval and the switching delay are small enough. Finally, two illustrative examples are presented to demonstrate the effectiveness of the results.

Robust fault estimation for uncertain switched linear systems with time-varying delay

The problem of fault estimation is investigated for a class of uncertain switched systems with time-varying delay. A robust observer-based fault estimator is designed such that the augment error system is exponentially stable and the H∞ performance index meets the predefined requirements. Based on the multiple Lyapunov-Krasovskii functions and the average dwell-time method, the delay dependent sufficient conditions on the existence of desired fault estimator are established. However, since these conditions are not linear matrix inequalities (LMIS), they can not be solved by MATLAB. By using a novel method, these conditions are presented in terms of LMIS. Finally, a numerical example is carried out. The designed fault estimator could tract the fault signal timely. Besides, the error between estimation and fault is very small. Therefore, the validity of the obtained results is illustrated.

Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects

This paper is concerned with the problem of exponential stability for a class of impulsive switched nonlinear time-delay systems with delayed impulse effects. By using the multiple Lyapunov–Krasovskii functionals technique, some exponential stability criteria are obtained, respectively, for two kinds of impulsive signals (destabilizing impulsive signal and stabilizing impulsive signal). The derived results not only characterise the effects of delayed impulse, time delay and switching on nonlinear systems, but also remove some restriction conditions. Furthermore, a more precise bound of system state is given. Compared with existing results on related problems, the obtained results are less conservative. Three examples are provided to illustrate the effectiveness and the generality of the proposed results.

Observer-based control for switched networked control systems with missing data

This paper addresses the issue of observer-based control problem for a class of switched networked control systems (NCSs). In particular, by considering the packet loss and time delay in the network, a discrete-time switched system is formulated. Moreover, the packet loss in the network is assumed to occur in a random way, which is described by introducing Bernoulli distributed white sequences. First, results for the exponential stabilization of discrete-time switched NCSs without random packet loss is derived by using the average dwell time approach and multiple Lyapunov–Krasovskii function. Next, the attention is focused on designing an observer-based state feedback controller for NCSs with random packet loss which ensures that the resulting error system is exponentially stable. Further, the sufficient conditions for existence of control parameters are formulated in the form of linear matrix inequalities (LMIs) which can be easily solved by using some standard numerical packages. Also, the observer and control gains can be calculated by using the solutions of a set of LMIs. Finally, a numerical example based on DC motor model is provided to illustrate the applicability and effectiveness of the proposed design procedure.

H∞output tracking control for uncertain networked control systems via a switched system approach

SummaryIn this paper, the problem ofH∞output tracking control for networked control systems with random time delays and system uncertainties is investigated. Effective sampling instant that is tightly related with transmission delay from sensor to actuator is proposed to ensure that the random variable time delay is always shorter than one effective sampling period. By using both active time‐varying sampling period strategy and hybrid node‐driven mechanism, the switching instant is coincided with the effective sampling instant. An augmented time‐varying networked tracking system model is provided by including the output tracking error as an additional state. However, random transmission delay causes indeterminate sampling period, which induces infinite subsystems. Gridding approach is introduced to transform the continuous time axis into discrete‐time sequences, which guarantees the finite number of switching rules. By employing multiple Lyapunov–Krasovskii functions, linear matrix inequality (LMI)‐based output trackingH∞performance analysis is presented, and robust switchingH∞model reference tracking controller for networked control systems with communication constraints and system uncertainties is designed to guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. Finally, simulation results illustrate the correctness and effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.

Network-Based Finite-time Sampled-data Observer Design for Switched Linear Systems

This paper is concerned with network-based sampled-data observer design problem for a class of switched linear systems in the finite-time H∞ sense. Outputs sampling and the detection of mode variations are both performed via a clock-driven approach, and networkinduced limitations involving transmission delays and data packet dropouts are also taken into account. Moreover, we introduce a novel multiple Lyapunov-Krasovskii functional, which switches along with the switching signals of the observer. The aforementioned technique can effectively reduce the complexity of the observer design procedures induced by the clock-driven detection scheme of mode variations. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.

Switching design of stabilising switched neutral systems with application to lossless transmission lines

The authors study the problem of asymptotically stabilising a class of switched neutral systems whose states cannot be directly measured. A state observer for each individual subsystem is constructed, based on which a switching law and a switching controller are designed. The designed switching law sufficiently considers the delayed states information. The authors adopt the multiple Lyapunov–Krasovskii functionals method to obtain a sufficient solvability condition for stabilisation which possesses less conservativeness. The authors also extend this method to stabilise switched neutral systems with time-varying structural uncertainties. Two examples are given to demonstrate the effectiveness of the authors’ proposed method.

Input-to-state stability of impulsive switched hybrid time-delay systems with delayed impulse effects

The input-to-state stability (ISS) and integral input-to-state stability (iISS) problems are addressed for a family of impulsive switched hybrid time-delay systems with delayed impulses. Employing the multiple Lyapunov–Krasovskii functionals method, sufficient conditions are established guaranteeing the ISS/iISS property of the given system. Here, the discrete dynamics are destabilizing (stabilizing) while the continuous dynamics may be stable (unstable). The impulsive, switching signals and delayed impulses are all considered which satisfy some dwell-time conditions. Two illustrative examples are presented to show that the proposed results are effective and a practical example is given to show a background of our model.

Observer‐based dissipative control for networked control systems: A switched system approach

This article studies the problem of observer‐based dissipative control problem for wireless networked control systems (NCSs). The packet loss and time delay in the network are modeled by a set of switches, using that a discrete‐time switched system is formulated. First, results for the exponential dissipativity of discrete‐time switched system with time‐varying delays are proposed by using the average dwell time approach and multiple Lyapunov–Krasovskii function. Then, the results are extended to drive the controller design for considered wireless NCS. The attention is focused on designing an observer‐based state feedback controller which ensures that, for all network‐induced delay and packet loss, the resulting error system is exponentially stable and strictly dissipative. The sufficient conditions for existence of controllers are formulated in the form of linear matrix inequalities (LMIs), which can be easily solved using some standard numerical packages. Both observer and controller gains can be obtained by the solutions of set of LMIs. Finally, numerical examples are provided to illustrate the applicability and effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 297–308, 2015

Exponential L 2-L ∞ filtering for a class of stochastic system with Markovian jump parameters and mixed mode-dependent time-delays

This paper discusses the exponential L2-L∞ filtering problem of a class of nonlinear stochastic systems with Markovian jumping parameters and mixed mode-dependent time-varying delays. By introducing a new multiple mode-dependent Lyapunov-Krasovskii functional, stochastic analysis is conducted. The condition for the existence of mode-dependent L2-L∞ filter, in which the filtering error is guaranteed to be exponentially stable with prescribed L2-L∞ performance, is developed. The developed criterion is delay-range-dependent, mode-dependent and decay-rate-dependent. Based on the derived criterion, the L2-L∞ filtering problems are solved. The mode-dependent filter coefficients can be obtained by solving a set of linear matrix inequalities (LMIs). Numerical simulations are presented to illustrate the effectiveness of the proposed approach.

Exponential Stability of Nonlinear Impulsive and Switched Time-Delay Systems with Delayed Impulse Effects

The exponential stability problem is considered for a class of nonlinear impulsive and switched time-delay systems with delayed impulse effects by using the method of multiple Lyapunov—Krasovskii functionals. Lyapunov-based sufficient conditions for exponential stability are derived, respectively, for stabilizing delayed impulses and destabilizing delayed impulses. It is shown that even if all the subsystems governing the continuous dynamics without impulse input delays are not exponential stable, if impulsive and switching signal satisfy a dwell-time upper bound condition, stabilizing delayed impulses can stabilize the systems in the exponential stability sense. Moreover, it is also shown that if the magnitude of the delayed impulses is sufficiently small, the exponential stability properties can be derived irrespective of the size of the impulse input delays under some conditions. The opposite situation is also developed. The efficiency of the proposed results is illustrated by two numerical examples.

Periodically intermittent control on robust exponential synchronization for switched interval coupled networks

This paper investigates the problem of robust synchronization for switched coupled interval networks via intermittent control. Based on the theories of the switched systems and coupled interval networks, the mathematical model of the switched coupled networks with uncertain parameters is established, the switched coupled interval networks consist of m modes and the interval networks switch from one mode to another according to a switch rule. By applying the average dwell time approach, structuring multiple Lyapunov–Krasovskii functions, and using Halanay inequality, new synchronization criteria are obtained for switched coupled networks with uncertain parameters. Moreover, as a special case, the obtained results can be used to check robust synchronization for coupled networks with uncertain parameters. Finally, an illustrative example is provided to demonstrate the validity of the theoretical results.

Robust Observer Design for Switched Positive Linear System with Uncertainties

This paper is concerned with the design of a robust observer for the switched positive linear system with uncertainties. Sufficient conditions of building a robust observer are established by using the multiple copositive Lyapunov-krasovskii function and the average dwell time approach. By introducing an auxiliary slack variable, these sufficient conditions are transformed into LMI (linear matrix inequality). A numerical example is given to illustrate the validities of obtained results.

Stochastic Finite-TimeH∞Performance Analysis of Continuous-Time Systems with Random Abrupt Changes

The problem ofH∞control performance analysis of continuous-time systems with random abrupt changes is concerned in this paper. By employing an augmented multiple mode-dependent Lyapunov-Krasovskii functional and using some integral inequalities, new sufficient conditions are obtained relating to finite-time bounded and anH∞performance index. The finite-timeH∞control performance problem is solved and desired controller is given to ensure the system trajectory stays within a prescribed bound during a given time interval. At last, two numerical examples are provided to show that our results are less conservative than the existing ones.

Switched exponential state estimation and robust stability for interval neural networks with the average dwell time

This paper is concerned with the problem of the exponential state estimation for switched neural networks with uncertain parameters. Based on the theories of the switched systems and available output measurements, the mathematical model of the switched interval estimation error system under the switching rule with average dwell time is established. Multiple Lyapunov–Krasovskii functions are employed to ensure the stability of the switched estimation error system for all admissible time delays; both the existence conditions and the explicit characterization of the desired estimator are derived in terms of linear matrix inequalities. Moreover, the sufficient conditions for guaranteeing the robust exponential stability of switched interval neural networks with discrete and distributed time delays are easily derived. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.