Time-varying Norm-bounded Parameter Uncertainties Research Articles

Design of Robust Dynamic Output Feedback Event-Triggering Controllers for Nonlinear Uncertain Systems

This paper presents a design of dynamic output feedback event-triggering control for nonlinear uncertain networked control systems. The plant and actuator asynchronously transmit the measurement and control signals over two different communication channels. We address the norm-bounded time-varying parameter uncertainties in a nonlinear plant. First, considering the exogenous disturbances and noises in the control and measurement signals, sufficient conditions for the <i>L</i>₂ stability of the nonlinear networked control systems are given in the presence of the uncertainties. Then, we propose design conditions to choose the dynamic output feedback control and triggering laws in terms of linear matrix inequalities (LMIs). The proposed conditions enable the controller and event-triggering parameters to be jointly optimized to lessen the number of transmissions, guaranteeing a certain level of <i>L</i>₂ gain. Numerical examples demonstrate the effectiveness of the proposed method.

Passivity-based non-fragile control of a class of uncertain fractional-order nonlinear systems

This article investigates the issues of passivity and feedback passification of a class of fractional-order (FO) nonlinear systems with time-varying norm-bounded parameter uncertainties in both the state and output matrices. Firstly, new passivity conditions presented by linear matrix inequalities (LMIs) are established based on new notions of passivity of FO systems. Secondly, considering inaccuracies or uncertainties may occur during controller implementation, non-fragile state feedback passification controller is proposed when the states are available. The obtained results extend and improve some recent results. Finally, the applicability and effectiveness of the developed results are examined via numerical examples with simulation results.

Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems

This paper addresses the guaranteed cost control problem of a class of uncertain fractional-order (FO) delayed linear systems with norm-bounded time-varying parametric uncertainty. The study is focused on the design of state feedback controllers with delay such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Stemming from the linear matrix inequality (LMI) approach and the FO Razumikhin theorem, a delay- and order-dependent design method is proposed with guaranteed closed-loop stability and cost for admissible uncertainties. Examples illustrate the effectiveness of the proposed method.

Robust H∞ controller design for uncertain 2D continuous systems with interval time-varying delays

ABSTRACTThe design of delay-dependent robust controllers is solved here for a class of uncertain 2D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov–Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to performance analysis and robust controller design, using linear matrix inequalities (LMIs). Two numerical examples are presented that illustrate the effectiveness of the proposed method.

Robust dissipativity and dissipation of a class of fractional‐order uncertain linear systems

This study addresses robust QSR-dissipativity and feedback dissipation of a class of fractional-order (FO) uncertain linear systems. Both the state and controlled output matrices are with time-varying norm-bounded parameter uncertainties. Firstly, some new notions of QSR-dissipativity and passivity for FO systems are introduced, the relationship between QSR-dissipativity and asymptotic stability and input-output stability are discussed, respectively. Then, a sufficient condition in the form of linear matrix inequality (LMI) is proposed to ensure that such system is robustly QSR-dissipative. According to this condition, a state feedback controller is proposed when the full states can be measured. Secondly, by employing LMI techniques and matrices singular value decomposition, sufficient conditions for the existence and a robust dissipation synthesis method are derived, respectively. Thirdly, a design method of dynamic output feedback controller is developed in order to guarantee that the closed-loop system is dissipative. Finally, some numerical examples are provided to show the application of the proposed methods.

Robust passivity and feedback passification of a class of uncertain fractional-order linear systems

ABSTRACTTheoretical results on robust passivity and feedback passification of a class of uncertain fractional-order (FO) linear systems are presented in the paper. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output matrices. Firstly, some suitable notions of passivity and dissipativity for FO systems are proposed, and the relationship between passivity and stability is obtained. Then, a sufficient condition in the form of linear matrix inequality (LMI) for such system to be robustly passive is given. Based on this condition, the design method of state feedback controller is proposed when the states are available. Moreover, by using matrix singular value decomposition and LMI techniques, the existing condition and method of designing a robust observer-based passive controller for such systems are derived. Numerical simulations demonstrate the effectiveness of the theoretical formulation.

Path following of a surface ship sailing in restricted waters under wind effect using robust H∞ guaranteed cost control

The path following problem of a ship sailing in restricted waters under wind effect is investigated based on Robust H∞ Guaranteed Cost Control (RHGCC). To design the controller, the ship maneuvering motion is modeled as a linear uncertain system with norm-bounded time-varying parametric uncertainty. To counteract the bank and wind effects, the integral of path error is augmented to the original system. Based on the extended linear uncertain system, sufficient conditions for existence of the RHGCC are given. To obtain an optimal robust H∞ guaranteed cost control law, a convex optimization problem with Linear Matrix Inequality (LMI) constraints is formulated, which minimizes the guaranteed cost of the close-loop system and mitigates the effect of external disturbance on the performance output. Numerical simulations have confirmed the effectiveness and robustness of the proposed control strategy for the path following goal of a ship sailing in restricted waters under wind effect.

Improved Results on Delay-Dependent $$H_\infty $$ H ∞ Control for Uncertain Systems with Time-Varying Delays

This paper deals with the problem of delay-dependent robust $$H_\infty $$Hź control for uncertain systems with time-varying delays and norm-bounded parameter uncertainties. Firstly, some new delay-dependent stability criteria are proposed by exploiting a new Lyapunov---Krasovskii functional and free-weighting matrices method. Secondly, based on the criteria obtained, a delay-dependent criterion for the existence of a memoryless state feedback $$H_\infty $$Hź controller that ensures asymptotic stability and a prescribed $$H_\infty $$Hź performance level of the closed-loop system for all admissible uncertainties is proposed in terms of linear matrix inequalities (LMIs). These developed results enjoy much less conservatism than the existing ones due to the introduction of delay segmentation approach to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms that take into account information of the time-delay. Finally, numerical examples are provided to demonstrate the effectiveness and benefits of the proposed method.

Delay decomposition approach to robust delay-dependent H∞ filtering of uncertain stochastic systems with time-varying delays

This paper presents the robust delay-dependent [Formula: see text] filter design for uncertain stochastic systems with time-varying delay. The systems under consideration are subject to time-varying norm-bounded parameter uncertainties and time-varying delays in both the state and measurement equations. The aim is to design a stable full-order linear filter assuring robustly asymptotical stability in mean-square and a prescribed [Formula: see text] performance level for the filtering error systems. Based on the delay decomposition approach and a new integral inequality, delay-dependent sufficient conditions for the existence of [Formula: see text] filters are proposed in terms of linear matrix inequalities. Finally, two numerical examples demonstrate that the proposed approaches are effective and are an improvement over existing ones.

Non-Fragile $$H_{\infty }$$ H ∞ Filter Design for Uncertain Stochastic Nonlinear Time-Delay Markovian Jump Systems

This paper investigates the problem of non-fragile and mode-dependent $$H_{\infty }$$ H ? filter design for a class of nonlinear stochastic Markovian jump systems with mode-dependent time-varying delays and norm-bounded parameter uncertainties. The non-fragile and mode-dependent filter to be designed is assumed to include multiplicative gain variations which result from inaccuracies in filter implementation, and the desired filter ensures the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed $$H_{\infty }$$ H ? -norm level for all admissible uncertainties. A stochastic Lyapunov---Krasovskii function is proposed to reflect the information of Markovian jump modes and the mode-dependent time-varying delays, and a set of strict linear matrix inequalities are utilized to derive sufficient conditions that guarantee the desired filter can be constructed. A numerical example and a vertical take-off and landing (VTOL) helicopter system are utilized to illustrate the effectiveness and usefulness of the main results obtained.

Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays

This paper is concerned with the passivity analysis problem for a class of discrete-time stochastic bidirectional associative memory neural networks with time-varying delays. Furthermore, the results are extended to the robust passivity analysis with mixed time delays that consist of both the discrete and distributed time delays, and the uncertainties are assumed to be time-varying norm bounded parameter uncertainties. By constructing a new Lyapunov---Krasovskii functional and introducing some appropriate free-weighting matrices, a delay-dependent passivity criterion is derived in terms of LMIs whose feasibility can be easily checked by some available software packages. Finally, two numerical examples with simulation results are given to demonstrate the effectiveness and usefulness of the proposed results.

Improved stochastic dissipativity of uncertain discrete-time neural networks with multiple delays and impulses

This paper investigates the problem of global dissipativity and global exponential dissipativity for a class of uncertain discrete-time stochastic neural networks with multiple time-varying delays. Here the multiple time-varying delays are assumed to be discrete and distributed and the uncertainties are assumed to be time-varying norm-bounded parameter uncertainties. By choosing a novel Lyapunov functional, combining with linear matrix inequality technique (LMI), Jensen’s inequality and stochastic analysis method, a new delay-dependent global dissipativity criterion is obtained in the form of LMI, which can be easily verified numerically using the effective LMI toolbox in Matlab. One important feature presents in our paper is that without employing model transformation and free weighting matrices our obtained result leads to less conservatism. Two illustrative examples are given to show the usefulness of the obtained dissipativity conditions.

Robust Estimation for Discrete Time-Varying Uncertain Systems with Observation Losses in Networked Control System

In this paper, we deal with the robust minimum variance filtering problem for discrete time-varying systems with observation losses. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in both the state and output matrices, and the observation losses are described by a Bernoulli process with a known probability. An upper bound on the variance of the state estimation error is first found under certain probability of missing observations and admissible parameter uncertainties. Then, a robust filter is derived by minimizing the prescribed upper bound in the sense of the matrix norm. It is shown that the desired filter can be obtained in terms of the solutions to two discrete Riccati difference equations.

RobustH∞Filtering for a Class of Uncertain Markovian Jump Systems with Time Delays

This paper studies the problem of robustH∞filtering for a class of uncertain time-delay systems with Markovian jumping parameters. The system under consideration is subject to norm-bounded time-varying parameter uncertainties. The problem to be addressed is the design of a Markovian jump filter such that the filter error dynamics are stochastically stable and a prescribed bound on theℒ2-induced gain from the noise signals to the filter error is guaranteed for all admissible uncertainties. A sufficient condition for the existence of the desired robustH∞filter is given in terms of two sets of coupled algebraic Riccati inequalities. When these algebraic Riccati inequalities are feasible, the expression of a desiredH∞filter is also presented. Finally, an illustrative numerical example is provided.

H∞Control for Stochastic Systems with Markovian Switching and Time-Varying Delay via Sliding Mode Design

This paper addresses the problem ofH∞control for a class of uncertain stochastic systems with Markovian switching and time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties and an unknown nonlinear function in the state. An integral sliding surface corresponding to every mode is first constructed, and the given sliding mode controller concerning the transition rates of modes can deal with the effect of Markovian switching. The synthesized sliding mode control law ensures the reachability of the sliding surface for corresponding subsystems and the global stochastic stability of the sliding mode dynamics. A simulation example is presented to illustrate the proposed method.

On design of robust reliable [formula omitted] control and input-to-state stabilization of uncertain stochastic systems with state delay

This paper is concerned with the problem of designing a robust reliable H∞ control for uncertain stochastic systems with time delay (USSD) and time-varying norm-bounded parametric uncertainties in the system states. The faulty actuators are considered as a disturbance signal to the system which is augmented with system disturbance input. The main objective of the paper is presenting a state feedback controller that guarantees input-to-state stability (ISS) of the plant and an H∞ norm-bound constraint on the attenuation of the augmented disturbance for all admissible uncertainties and actuator failures. The problem is solved by using Lyapunov functions together with the Razumikhin methodology. To clarify the proposed results, some illustrative examples are presented.

Stability of Discrete Recurrent Neural Networks with Interval Delays

A global exponential stability method for a class of discrete time recurrent neural networks with interval time-varying delays and norm-bounded time-varying parameter uncertainties is developed in this paper. The method is derived based on a new Lyapunov-Krasovskii functional to exhibit the delay-range-dependent dynamics and to compensate for the enlarged time-span. In addition, it eliminates the need for over bounding and utilizes smaller number of LMI decision variables. Effective solutions to the global stability problem are provided in terms of feasibility-testing of parameterized linear matrix inequalities (LMIs). Numerical examples are presented to demonstrate the potential of the developed technique.

Design of a robust controller on stabilization of stochastic neural networks with time varying delays

This paper is concerned with the problem of robust stabilization and H∞ control for a class of uncertain stochastic neural networks with time-varying delays and time-varying norm-bounded parameter uncertainties. The delay is of a time-varying nature, and the activation functions are assumed to be neither differentiable nor strictly monotonic. Moreover, the description of the activation functions is more general than the commonly used Lipschitz conditions. By using the Lyapunov function approach together with the linear matrix inequality (LMI) technique, for the robust stabilization we propose a state feedback controller to ensure that the closed loop system is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. For the robust H∞ control problem, a state feedback controller is designed such that in addition to the requirement of robust stability, a prescribed H∞ performance level is to be satisfied. The results obtained are formulated in terms of LMIs which can be easily checked by the MATLAB LMI control toolbox. Numerical examples are presented to illustrate the effectiveness of the obtained method and the improvement over some existing results.

Robust passivity analysis of a class of discrete-time stochastic neural networks

This paper addresses the passivity problem of a class of discrete-time stochastic neural networks with time-varying delays and norm-bounded parameter uncertainties. New delay-dependent passivity conditions are obtained by using a novel Lyapunov functional together with the linear matrix inequality approach. Numerical examples show the effectiveness of the proposed method.

Robust H ∞ filter design of uncertain T-S fuzzy neutral systems with time-varying delays

This article addresses the problem of robust H ∞ filter design of a class of Takagi–Sugeno fuzzy neutral systems with time-varying delays and norm-bounded parameter uncertainties. A fuzzy filter is constructed, which ensures both the robust stability and a prescribed H ∞ performance of the filtering error system. A linear matrix inequality approach is developed, and a delay-dependent sufficient condition is obtained. A simulation example is provided to demonstrate the effectiveness of the proposed approach.