Robust H-infinity estimation for continuous-time polytopic uncertain systems

The design of full-order robust H-infunity estimators is investigated for continuous-time polytopic uncertain systems, The main purpose is to obtain a stable and proper linear estimator such that the estimation error system remains robustly stable with a prescribed H-infinity attenuation level. Based on a recently proposed H-infinity performance criterion which exhibits a kind of decoupling between the Lyapunov matrix and the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.

Enhanced LMI Representations for H2 Performance of Polytopic Uncertain Systems: Continuous-time Case

Based on two recent results, several new criteria of H2 performance for continuous-time linear systems are established by introducing two slack matrices. When used in robust analysis of systems with polytopic uncertainties, they can reduce conservatism inherent in the earlier quadratic method and the established parameter-dependent Lyapunov function approach. Two numerical examples are included to illustrate the feasibility and advantage of the proposed representations.

Robust dissipative filtering for continuous-time polytopic uncertain time-delay systems

This paper focuses on the problem of dissipative filtering for linear continuous-time polytopic uncertain time-delay systems. To obtain a stable and proper linear filter such that the filtering error system is strictly dissipative for all admissible uncertainties,a new dissipativity criterion which realizes separation between the Lyapunov matrices and the system dynamic matrices is firstly provided in terms of linear matrix inequalities ( LMI) . Then an LMI sufficient condition for the existence of a robust filter is established and a design procedure is proposed for this type of systems. One numerical example demonstrates less conservativeness of the proposed criterion,the other numerical example illustrates the validity of the proposed filter design.

Robust dissipative filtering for continuous-time polytopic uncertain neutral systems

This article is concerned with the problem of robust dissipative filtering for continuous-time polytopic uncertain neutral systems. The main purpose is to obtain a stable and proper linear filter such that the filtering error system is strictly dissipative. A new criterion for the dissipativity of neutral systems is first provided in terms of linear matrix inequalities （LMI）. Then, an LMI sufficient condition for the existence of a robust filter is established and a design procedure is proposed for this type of systems. Two numerical examples are given. One illustrates the less conservativeness of the proposed criterion; the other demonstrates the validity of the filtering design procedure.

Robust H_∞ Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback

In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.

Parameter-dependent Lyapunov functional for systems with multiple time delays

The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between die terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.

Robust H-infinity filtering for time-delaysystems with missing measurements:a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities （LMIs）. When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.

New Results on Stability and Stabilization of Delayed Caputo Fractional Order Systems with Convex Polytopic Uncertainties

In this paper,the problems of robust stability and stabilization,for the first time,are studied for delayed fractional-order linear systems with convex polytopic uncertainties.The authors derive some sufficient conditions for the problems based on linear matrix inequality technique combined with fractional Razumikhin stability theorem.All the results are obtained in terms of linear matrix inequalities that are numerically tractable.The proposed results are quite general and improve those given in the literature since many factors,such as discrete and distributed delays,convex polytopic uncertainties,global stability and stabilizability,are considered.Numerical examples and simulation results are given to illustrate the effectiveness of the effectiveness of our results.

Robust H-infinity filter for a class of polytopic Delta operator systems

This study deals with the robust H-infinity filtering for a class of Delta operator systems with polytopic uncertainties. By the aid of introducing two slack matrices to eliminate the coupling between systems matrices and Lya- punov matrices, an improved version of the bounded real lemma is given via linear matrix inequality formulation, which shows a close correspondence between the continuous- and discrete-time H-infinity performance criterion. Based on it, the existence condition of the desired filter is obtained such that the corresponding filtering error system is asymptotically stable with a guaranteed performance index. A numerical example is employed to illustrate the feasibility and advantages of the orooosed design.

Relaxed delay-dependent exponential stability condition for a class of neural networks with polytopic uncertainties and distributed delays

The global robust exponential stability of a class of neural networks with polytopic uncertainties and distributed delays is investigated in this paper.Parameter-dependent Lypaunov-Krasovskii functionals and free-weighting matrices are employed to obtain sufficient condition that guarantee the robust global exponential stability of the equilibrium point of the considered neural networks.The derived sufficient condition is proposed in terms of a set of relaxed linear matrix inequalities (LMIs),which can be checked easily by recently developed algorithms solving LMIs.A numerical example is given to demonstrate the effectiveness of the proposed criteria.

Mixed H_2/H_∞ filtering for a class of high-speed sampling uncertain systems

The problem of mixed H2/H∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H2/H∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H2/H∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility of the proposed approach.

Fault Detection of Networked Control Systems with Uncertain Time-Varying Delay and Quantization Error

Problems related to fault detection of networked control systems (NCSs) with both uncertain time-varying delay and quantization error are studied in this paper. A novel model with the form of polytopic uncertainty is given to represent the influences of both the time-varying delay and the quantization error, and then the reference model based method is used to design the residual generator that is robust to both unknown network-induced delay and unknown inputs. A numerical example is also given to illustrate the merits of the presented method. The proposed method can be regarded as an extension of the authors' former work, which can only deal with time-varying delay.

Design of mixed H-two/H-infinity optimal control systems using multiobjective differential evolution algorithm

In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective opti-mization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building a LMIs-based synthesis algorithm, a self-adaptive control parameter multiobjective differential evolution algorithm is developed directly in the controller parameters space. In the case of systems with polytopic uncertainties, the worst case norm computation is formulated as an implicit optimization problem, and the proposed self-adaptive differential evolution is employed to calculate the worst case H-two and H-infinity norms. The numerical examples illustrate the power and validity of the proposed approach for the mixed H-two/H-infinity control multiobjective optimal design.

Sampling Dependent Stability Results for Aperiodic Sampled-Data Systems

This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent,and not imposed to be definite positive.Based on the system information on the sampling interval wholly rather than partly,a new Lyapunovlike functional is constructed,which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state.To take advantage of the integral of the system state,integral equations of the sampled-data system are explored when estimating the derivative of the extended functional.By the Lyapunov-like functional theory,a new sampling dependent stability result is obtained for sampled-data systems without uncertainties.Then,the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived.At last,numerical examples are given to illustrate that the stability results improve over some existing ones.

Robust state feedback for uncertain 2-D discrete switched systems in the Roesser model

The design of robust H_(∞)controllers is considered here for a class of two-dimensional(2-D)discrete switched systems described by the Roesser model with polytopic uncertainties.Attention focuses on the design of a switched state feedback controller,which guarantees the robust asymptotic stability and a prescribedH_(∞)performance for the closed-loop system.By using multiple parameter-dependent Lyapunov functionals,and introducing some switched free-weighting matrices,a new sufficient condition for the robust H_(∞)performance analysis of uncertain 2-D discrete switched systems is developed.Furthermore,the design of switched state feedback controller is proposed in terms of linear matrix inequalities(LMIs).Illustrative examples are given to illustrate the effectiveness of the developed theoretical results.