Robust H∞ non-fragile controller design for uncertain descriptor systems with time-varying discrete and distributed delays

This paper is concerned with the design problem of non-fragile H ∞ controller for uncertain descriptor systems with time-varying discrete and distributed delays and controller gain variations. The designed controller is shown to be robust not only to parameter uncertainties, but also to errors in the controller coefficients. The obtained criterion to derive an efficient non-fragile H∞ control design is expressed as a set of nonconvex matrix inequalities, which can be solved by combining both linear matrix inequalities technique and cone complementarity method. A numerical example is given to demonstrate effectiveness of the proposed methods

Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and markovian switching

The problem of delay-dependent stability in the mean square sense for stochastic systems with time-varying delays, Markovian switching and nonlinearities is investigated. Both the slowly time-varying delays and fast time-varying delays are considered. Based on a linear matrix inequality approach, delay-dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result. Numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature

Absolute stability of Lur'e systems with time-varying delay

The problem of the absolute the stability of Lur'e systems with time-varying delay is addressed. Full consideration is given to two cases of time-varying delays - one being continuous-uniformly bounded and the other being differentiable-uniformly bounded with the derivative of the delay bounded by a constant. Some delay-dependent absolute-stability criteria are derived and formulated in the form of linear matrix inequalities. The relationship between the absolute stability criteria for the two cases of time-varying delays is built. A numerical example shows the effectiveness of the obtained results

Robust h-inf filter design of uncertain descriptor systems with discrete and distributed delays

The robust H-inf filtering problem for a class of continuous-time uncertain linear descriptor systems with time-varying discrete and distributed delays is investigated. The time delays are assumed to be constant and known. The uncertainties under consideration are norm-bounded, and possible time-varying, uncertainties. Sufficient condition for the existence of an H-inf filter is expressed in terms of strict linear matrix inequalities (LMIs). Instead of using decomposition technique, a unified form of LMIs is proposed to show the exponential stability of the augmented systems. The condition for assuring the stability of the “fast” subsystem is implied from the unified form of LMIs, which is shown to be less conservative than the characteristic equation based conditions or matrix norm-based conditions. The suitable filter is derived through a convex optimization problem. A numerical example is given to show the effectiveness of the method

Delayed feedback control of uncertain systems with time-varying input delay

This paper is concerned with a delayed feedback control design for uncertain systems with time-varying input delay. Based on a reduction method, a new control design method is proposed by introducing some relaxation matrices and turning parameters, which can be chosen properly to lead to a less conservative result. A numerical example is given to show the effectiveness and less conservativeness of the method

Stability of linear neutral systems with mixed delay and polytopic uncertainty

This paper is concerned with the stability of uncertain linear systems with mixed neutral and discrete delays. The uncertainty under consideration is of polytopic type. A new analysis approach which combines the descriptor system transformation and relaxation matrix is proposed to derive some less conservative stability criteria. The criteria are dependent on both neutral delay and discrete delay. Numerical examples are given to indicate improvements over some existing results

Network-based robust H∞ filtering for uncertain linear systems

The problem of network-based robust H∞ filtering for uncertain linear systems is investigated. Different from the design of the traditional filter, the effects of the network-induced delay and data dropout on the performance of a filtering-error system are considered. The derived criteria for H∞ performance analysis of the filtering-error system and filter design are expressed as a set of linear matrix inequalities, which can be solved by using convex optimization method. Numerical examples show the effectiveness of the design method

Delay-dependent robust H∞ controller design for uncertain descriptor systems with time-varying discrete and distributed delays

The design problem of a delay-dependent robust H1 controller for uncertain descriptor systems with time-varying discrete and distributed delays is investigated. The designed controller can guarantee the closed-loop system is regular, impulse-free and exponentially stable with an H1 norm bound constraint. The obtained criteria to derive an efficient robust H1 control design are expressed as a set of nonconvex matrix inequalities, which can be solved by combining both the linear matrix inequalities technique and the cone complementarity method. Two numerical examples are given to demonstrate effectiveness and less conservativeness of the proposed method

A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model

The real circuit model, such as a partial element equivalent circuit (PEEC), can be represented as a delay differential equation (DDE) of neutral type. The study of asymptotic stability of this kind of systems is of much importance due to the fragility of DDE solvers. Based on a descriptor system approach,new delay-dependent stability results are derived by introducing some free weighting matrices. As an application of the results, the delay-dependent stability problem of a PEEC model is investigated. The comparison of the esults with the existing ones is finally given by using the PEEC model and another numerical example

Robust H∞ filter design of uncertain descriptor systems with discrete and distributed delays

The robust H∞ filtering problem for a class of continuous-time uncertain linear descriptor systems with time-varying discrete and distributed delays is investigated. The time delays are assumed to be constant and known. The uncertainties under consideration are norm-bounded, and possible time-varying, uncertainties. Sufficient condition for the existence of an filter is expressed in terms of strict linear matrix inequalities (LMIs). Instead of using decomposition technique, a unified form of LMIs is proposed to show the exponential stability of the augmented systems. The condition for assuring the stability of the “fast” subsystem is implied from the unified form of LMIs, which is shown to be less conservative than the characteristic equation based conditions or matrix norm-based conditions. The suitable filter is derived through a convex optimization problem. A numerical example is given to show the effectiveness of the method