Time-varying Norm-bounded Parameter Uncertainties Research Articles

Robust Reliable Control for a class of Uncertain Switched Linear Systems

This paper is concerned with the problem of robust reliable H ∞ control for a class of uncertain switched systems with disturbances and also with actuator failures among a prespecified subset of actuator. Both state matrix and output matrix contain time-varying norm-bounded parameter uncertainties. The purpose of this problem is to design robust feedback-reliable controllers and a switching law such that the systems remain globally quadratically stable and H ∞ performance not only when all actuators are operational, but also when some actuators experience failures. A design approach based on LMI(linear matrix inequality) method and convex combination technique is proposed to solve the problem addressed. Finally, simulation results illustrate the validity of designed controllers and the switching law.

H ∞ Guaranteed Cost Filtering for Uncertain Discrete-Time Switched Systems With Multiple Time-Varying Delays

This paper deals with the problem of H∞ guaranteed cost filtering for uncertain discrete-time switched systems with multiple time-varying delays. The switched system under consideration is subject to time-varying norm-bounded parameter uncertainties in all the system matrices. The aim is to design a filter, which guarantees the asymptotical stability of the error system with prescribed disturbance attenuation for all admissible uncertainties and the cost function value is not more than a specified upper bound. By resorting to a switched Lyapunov function, some delay-dependent sufficient conditions are presented in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed algorithms.

Design of robust-optimal output feedback controllers for linear uncertain systems using LMI-based approach and genetic algorithm

This paper considers the robust-optimal design problems of output feedback controllers for linear systems with both time-varying elemental (structured) and norm-bounded (unstructured) parameter uncertainties. Two new sufficient conditions are proposed in terms of linear-matrix-inequalities (LMIs) for ensuring that the linear output feedback systems with both time-varying elemental and norm-bounded parameter uncertainties are asymptotically stable, where the mixed quadratically-coupled parameter uncertainties are directly considered in the problem formulation. A numerical example is given to show that the presented sufficient conditions are less conservative than existing ones reported recently. Then, by integrating the hybrid Taguchi-genetic algorithm (HTGA) and the proposed LMI-based sufficient conditions, a new integrative approach is presented to find the output feedback controllers of the linear systems with both time-varying elemental and norm-bounded parameter uncertainties such that the control objective of minimizing a quadratic integral performance criterion subject to the stability robustness constraint is achieved. A design example of the robust-optimal output feedback controller for the AFTI/F-16 aircraft control system with the time-varying elemental parameter uncertainties is given to demonstrate the applicability of the proposed new integrative approach.

Design of delay-range-dependent robust controller for uncertain genetic regulatory networks with interval time-varying delays

This paper investigates the problem of robust stabilization for genetic regulatory networks with interval time-varying delays, which are subject to norm-bounded time-varying parameter uncertainties. The time delays including lower and upper bounds of delay are assumed to appear in both the mRNA and protein. The regulatory functions are assumed to be globally Lipschitz continuous. The resulting delay-range-dependent robust controller with interval range is designed in terms of improved bounding technique. A sufficient condition for the solvability of the problem is obtained via a linear matrix inequality (LMI). When this LMI is feasible, an explicit expression of a desired state feedback controller is also given. The theory developed in this paper is demonstrated by two numerical examples.

New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays

This paper investigates the problem of passivity analysis for a class of uncertain discrete-time stochastic neural networks with mixed time delays. 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. By constructing a novel Lyapunov functional and introducing some appropriate free-weighting matrices, delay-dependent passivity analysis criteria are derived. Furthermore, the additional useful terms about the discrete time-varying delay will be handled by estimating the upper bound of the derivative of Lyapunov functionals, which is different from the existing passivity results. These criteria can be developed in the frame of convex optimization problems and then solved via standard numerical software. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.

Robust ℋ∞ control for networked control systems with uncertainties and multiple-packet transmission

A class of networked control systems is investigated where the plant has time-varying norm-bounded parameter uncertainties and both the sensor-to-controller and controller-to-actuator channels implement multiple-packet transmission and experience random packet dropouts. Sufficient conditions for synthesis of robust stochastic stabilisation and design of robust ℋ∞ controller are derived in the form of linear matrix inequalities. An example is provided to demonstrate the effectiveness of the proposed method.

Robust global stability of discrete-time recurrent neural networks

This paper establishes new delay-range-dependent, robust global stability for a class of discrete-time recurrent neural networks with interval time-varying delays and norm-bounded time-varying parameter uncertainties. A new Lyapunov-Krasovskii functional is constructed to exhibit the delay-dependent dynamics and compensate for the enlarged time-span. The developed stability method eliminates the need for over bounding and utilizes a smaller number of linear matrix inequality (LMI) decision variables. New and less conservative solutions to the global stability problem are provided in terms of feasibility testing of new parametrized LMIs. Numerical examples are presented to illustrate the effectiveness of the developed technique.

Robust H∞ filtering for uncertain Markovian jump systems with mode‐dependent distributed delays

AbstractThis paper deals with the problem of robust H∞ filter design for Markovian jump systems with norm‐bounded time‐varying parameter uncertainties and mode‐dependent distributed delays. Both the state and the measurement equations are assumed to be with distributed delays. Sufficient conditions for the existence of robust H∞ filters are obtained. Via solving a set of linear matrix inequalities, a desired filter can be constructed. The developed theory is illustrated by a simulation example. Copyright © 2009 John Wiley & Sons, Ltd.

Robust generalised ℋ2 and ℋ∞ static output feedback control for uncertain discrete-time fuzzy systems

This study is concerned with the generalised ℋ2 and the ℋ∞ static control problems for discrete-time fuzzy systems with time-varying norm-bounded parametric uncertainties. Based on the solutions to certain linear matrix inequalities LMIs, static output feedback controllers are designed, which can ensure the asymptotic stability and the generalised ℋ2 and ℋ∞ performance level, respectively. Differenting from the existing results, the design conditions in this study are derived in terms of LMIs directly, and the local output matrices are allowed to be different. Three illustrative examples are provided to demonstrate the effectiveness and the reduced conservatism of the proposed methods.

Exponential estimates for stochastic delay equations with norm-bounded uncertainties

This paper presents the sufficient conditions for the exponential stability of linear or semilinear stochastic delay equations with time-varying norm bounded parameter uncertainties. Exponential estimates for the solutions are also obtained by using a modified Lyapunov-Krasovski functional. These conditions can be tested numerically using interior point algorithms.

Delay-Range-Dependent Global Robust Passivity Analysis of Discrete-Time Uncertain Recurrent Neural Networks with Interval Time-Varying Delay

This paper examines a passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with norm-bounded time-varying parameter uncertainties and interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. Based on an appropriate type of Lyapunov functional, sufficient passivity conditions for the DRNNs are derived in terms of a family of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness and applicability.

Robust [formula omitted] control with maximal decay rate for linear discrete-time stochastic systems

The problems of robust stabilization and robust H ∞ control with maximal decay rate are investigated for discrete-time stochastic systems with time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, an optimal state feedback controller is designed, which ensures that the closed-loop system is robustly stochastically stable with maximal decay rate, while for the robust H ∞ control problem, the designed state feedback controller guarantees that the resulting closed-loop system is with a specified H ∞ performance level, besides robust stochastic stability with maximal decay rate. The method based on the convex optimization and linear matrix inequality is developed to solve these problems. Two examples are provided to show the effectiveness of the proposed approach.

Linear matrix inequality-based robust H∞ control of sampled-data systems with parametric uncertainties

The problem of robust H∞ controller design for sampled-data systems with time-varying norm-bounded parameter uncertainties in the state matrices is investigated. Attention is focused on the design of a causal sampled-data controller which guarantees the asymptotical stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed H∞ performance bound for all admissible uncertainties. Sufficient condition for the solvability of the problem is in terms of linear matrix inequalities (LMIs) technique. It is shown that the desired H∞ controller can be constructed by solving certain LMIs. An illustrative example is given to demonstrate the effectiveness of the proposed method.

A Delay-Dependent Approach to Passivity Analysis for Uncertain Neural Networks with Time-varying Delay

This paper deals with the problem of passivity analysis for neural networks with time-varying delay, which is subject to norm-bounded time-varying parameter uncertainties. The activation functions are supposed to be bounded and globally Lipschitz continuous. Delay-dependent passivity condition is proposed by using the free-weighting matrix approach. These passivity conditions are obtained in terms of linear matrix inequalities, which can be investigated easily by using standard algorithms. Two illustrative examples are provided to demonstrate the effectiveness of the proposed criteria.

A delay-range-dependent approach to global robust stability for discrete-time uncertain recurrent neural networks with interval time-varying delay

The current paper performs a global robust stability analysis for a class of discrete-time recurrent neural networks (DRNNs) with norm-bounded time-varying parameter uncertainties and interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. An appropriate type of Lyapunov functional is proposed to establish the sufficient conditions for the DRNNs. The criteria are formulated by means of the feasibility of linear matrix inequalities (LMIs), which can be easily checked in practice. Two numerical examples are given to illustrate the effectiveness and applicability.

Robust exponential stability of uncertain discrete time impulsive switching systems with state delay

A new class of hybrid impulsive and switching models are introduced and their robust exponential stability and control synthesis are addressed. The proposed switched system is composed of stable subsystems and unstable subsystems, which not only involves state delay and norm-bounded time-varying parameter uncertainties, but also contains the impulsive switching effects between the subsystems. Based on the extension of the system dimension and the concept of average dwell time, a kind of practically useful switching rule is presented which guarantees the desired robust exponential stability. A switched state feedback controller is also given.

Robust stability of uncertain discrete-time singular fuzzy systems

This paper considers the problem of robust stability analysis of uncertain discrete-time singular fuzzy systems described by a class of extended Takagi–Sugeno fuzzy dynamic models with time-varying norm-bounded parameter uncertainties. A sufficient condition ensuring a discrete singular fuzzy system to be regular, causal and stable is proposed in terms of a set of linear matrix inequalities. Based on this, a robust stability condition is obtained. Both of these conditions can be checked by using recently developed algorithms in solving LMIs. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.

Decentralised reliable guaranteed cost control of uncertain systems: an LMI design

The problem of designing a decentralised control scheme for a class of linear large scale interconnected systems with norm-bounded time-varying parameter uncertainties under a class of control failures is addressed. These failures are described by a model that considers possible outages or partial failures in every single actuator of each decentralised controller. The control design is performed through two steps. First, a decentralised reliable guaranteed cost control set is derived and, second, a feasible linear matrix inequalities procedure is presented for the effective construction of the control set. A numerical example illustrates the efficiency of the proposed control scheme.

A New Approach to Robust H∞ Filtering for Uncertain Systems with Both Discrete and Distributed Delays

This paper is concerned with robust H∞ filter design for a class of linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both state and measurement equations. A new design method is proposed by introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. A sufficient condition is obtained to guarantee the existence of desired H∞ filters, which can be constructed by solving a convex optimization problem. A numerical example is included to illustrate the effectiveness and the reduced conservatism of the proposed design technique.

Delay-dependent output feedback guaranteed cost control for uncertain discrete-time systems with multiple time-varying delays

The dynamic output feedback guaranteed cost control problem is investigated for a class of uncertain discrete-time systems with multiple time-varying state delays and norm-bounded parameter uncertainties. Attention is focused on the design of the dynamic output feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Delay-dependent sufficient conditions for the existence of the desired guaranteed cost controllers are derived without involving model transformation and bounding technique for cross terms, and these conditions are formulated in terms of nonlinear matrix inequalities. An iterative algorithm involving convex optimisations is presented to solve these nonlinear matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.