Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements

In this paper, the robust H/sub /spl infin// filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. We aim to design filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable, and the prescribed H/sub /spl infin// performance constraint is met. In terms of certain linear matrix inequalities (LMIs), sufficient conditions for the solvability of the addressed problem are obtained. When these LMIs are feasible, an explicit expression of a desired robust H/sub /spl infin// filter is also given. An optimization problem is subsequently formulated by optimizing the H/sub /spl infin// filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.     

Robust H/sub /spl infin// filtering for Uncertain2-D continuous systems

This paper considers the problem of robust H/sub /spl infin// filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H/sub /spl infin// norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H/sub /spl infin// filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.     

Fixed-order robust H/sub /spl infin// filter design for Markovian jump systems with uncertain switching probabilities

This paper discusses the fixed-order robust H/sub /spl infin// filtering problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration are assumed to be norm-bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix, respectively. First, a criterion based on linear matrix inequalities is provided for testing the H/sub /spl infin// filtering level of a filter over all the admissible uncertainties. Then, a sufficient condition for the existence of the fixed-order robust H/sub /spl infin// filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints. To determine the filter, a globally convergent algorithm involving convex optimization is suggested. Finally, a numerical example is used to illustrate that the developed theory is more effective than the existing results.     

Design of reduced-order H/sub /spl infin// filter for Markovian jumping systems with time delay

This brief is concerned with the reduced-order H/sub /spl infin// filtering problem for Markovian jumping linear systems with time delay, where the jumping parameters are modeled by a discrete-time Markov process. Sufficient conditions for the existence of the reduced-order H/sub /spl infin// filter are proposed in terms of linear matrix inequalities (LMI) and a coupling nonconvex matrix rank constraint. In particular, the sufficient conditions for the existence of the zeroth-order (or static) H/sub /spl infin// filter can be expressed in terms of a set of strict LMIs. The explicit parameterization of the desired filter is also given. Finally, a numerical example is given to illustrate the proposed approach.     

An LMI approach to the H/sub /spl infin// filter design for uncertain systems with distributed delays

This paper investigates the problem of robust H/sub /spl infin// filter design for linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both the state and measurement equations. The problem we address is the design of a filter, such that for all admissible uncertainties, the resulting error system is asymptotically stable and satisfies a prescribed H/sub /spl infin// performance level. A sufficient condition is obtained to guarantee the existence of desired H/sub /spl infin// filters, which can be constructed by solving certain linear matrix inequalities. The effectiveness of the proposed design method is demonstrated by a numerical example.     

Robust filtering for discrete-time systems with saturation and its application to transmultiplexers

This paper considers the problem of robust filtering for discrete-time linear systems subject to saturation. A generalized dynamic filter architecture is proposed, and a filter design method is developed. Our approach incorporates the conventional linear H/sub 2/ and H/sub /spl infin// filtering as well as a regional l/sub 2/ gain filtering feature developed specially for the saturation nonlinearity and is applicable to the digital transmultiplexer systems for the purpose of separating filterbank design. It turns out that our filter design can be carried out by solving a constrained optimization problem with linear matrix inequality (LMI) constraints. Simulations show that the resultant separating filters possess satisfactory reconstruction performance while working in the linear range and less degraded reconstruction performance in the presence of saturation.     

Robust filtering for 2-D state-delayed systems with NFT uncertainties

This paper is concerned with the robust filtering problem for two-dimensional (2-D) state-delayed systems with uncertainties represented by nonlinear fraction transformation. The authors first establish the stability H/sub /spl infin// performance and generalized H/sub 2/ performance criteria for the system. Based on the results, the authors propose efficient methods to solve the robust H/sub /spl infin// filtering, generalized H/sub 2/ filtering, and mixed generalized H/sub 2//H/sub /spl infin// filtering problems by using a parameter-dependent Lyapunov function approach. The methods involve solving linear matrix inequalities. Two examples are given to show the effectiveness of the proposed approach.     

Reduced-order H/sub /spl infin// filtering for stochastic systems

This paper deals with the reduced-order H/sub /spl infin// filtering problem for stochastic systems. Necessary and sufficient conditions are obtained for the existence of solutions to the continuous-time and discrete-time problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. Furthermore, when these conditions are feasible, an explicit parametrization of all desired reduced-order filters corresponding to a feasible solution is given. In particular, when the reduced-order filter is restricted to be a static one, then simple conditions expressed by LMIs only without any rank constraints are derived, and a parametrization of all solutions is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.     

Genetic algorithm approach to fixed-order mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter designs

The mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter is proposed to achieve the H/sub 2/ optimal reconstruction and a desired robustness against the effect of uncertainties in signal processing from the H/sub /spl infin// norm perspective. However, the conventional mixed H/sub 2//H/sub /spl infin// optimal design filters are very complicated and are not practical for industrial applications. For simplicity of implementation and conservation of operation time, the fixed-order mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter design is interesting for engineers in signal processing from the practical design perspective. In this study, to avoid the trap of local minima, a design method based on the genetic algorithm is introduced to treat the nonlinear optimization design problem of the fixed-order mixed H/sub 2//H/sub /spl infin// deconvolution filter. The convergence property of our design algorithm is also discussed. Finally, an example is presented to illustrate the design procedure and confirm the robustness performance of the proposed method.     

Robust H/sub /spl infin// control of singular impulsive systems with uncertain perturbations

This paper discusses the problem of robust H/sub /spl infin// control for singular impulsive uncertain systems. Some new fundamental properties of singular systems with impulse effect are derived. Based on the Riccati inequality approach, sufficient conditions for robust H/sub /spl infin// criteria of the corresponding singular impulsive closed-loop systems are established. A simple approach to the design of a robust impulsive controller is then presented. Finally, a design example and simulation results are given to demonstrate the effectiveness of the proposed approach.     

Suboptimal reduced-order filtering through an LMI-based method

This paper addresses the reduced-order filtering design problem for continuous-time linear systems. The H/sub 2/ and H/sub /spl infin// norms of the estimation error, used as performance criteria, are discussed and a new linear matrix inequalities (LMI)-based method for reduced-order filter design is proposed. Differently from the methods available in the literature to date, the one presented here does not solve the associated nonconvex problem by means of an appropriate optimization procedure. It is based on the a priori determination of a certain matrix that simultaneously rends convex the problem to be solved and reduces the suboptimality degree of the solution. Its efficiency is tested by means of two examples. The first one, borrowed from the literature, allows the comparison of our method, for the H/sub 2/ norm case, with three earlier techniques, one of them being the well-known balanced truncation. The second one, of higher order, consists of the estimation of the displacement of a tapered bar using an H/sub /spl infin// norm criterion.     

Robust H/sub /spl infin// controller design with recurrent neural network for linear synchronous motor drive

In this paper, a robust controller design with H/sub /spl infin// performance using a recurrent neural network (RNN) is proposed for the position tracking control of a permanent-magnet linear synchronous motor. The proposed robust H/sub /spl infin// controller, which comprises a RNN and a compensating control, is developed to reduce the influence of parameter variations and external disturbance on system performance. The RNN is adopted to estimate the dynamics of the lumped plant uncertainty, and the compensating controller is used to eliminate the effect of the higher order terms in Taylor series expansion of the minimum approximation error. The tracking performance is ensured in face of parameter variations, external disturbance and RNN estimation error once a prespecified H/sub /spl infin// performance requirement is achieved. The synthesis of the RNN training rules and compensating control are based on the solution of a nonlinear H/sub /spl infin// control problem corresponding to the desired H/sub /spl infin// performance requirement, which is solved via a choice of quadratic storage function. The proposed control method is able to track both the periodic step and sinusoidal commands with improved performance in face of large parameter perturbations and external disturbance.     

Robust filtering for uncertain nonlinearly parameterized plants

We address the robust filtering problem for a wide class of systems whose state-space data assume a very general nonlinear dependence in the uncertain parameters. Our resolution methods rely on new linear matrix inequality characterizations of /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// performances, which, in conjunction with suitable linearization transformations of the variables, give rise to practical and computationally tractable formulations for the robust filtering problem.     

H/sub /spl infin// filtering for multiple-time-delay measurements

The aim of this paper is to study the H/sub /spl infin// filtering problem for linear continuous-time systems with both current and multiple-time-delay measurements. The key technique applied for deriving the filter is the reorganized innovation analysis approach in Krein space. A necessary and sufficient condition for the existence of an H/sub /spl infin// filter is derived, and the solution to the H/sub /spl infin// filter is given in terms of solutions of Riccati and matrix differential equations. An example is finally presented to show the effectiveness of the proposed approach.     

Design of Luenberger state observers using fixed-structure H/sub /spl infin// optimization and its application to fault detection in lane-keeping control of automated vehicles

Lane-keeping control forms an integral part of fully automated intelligent vehicle highway systems (IVHS) and its reliable operation is critical to the operation of an automated highway. We present the design of a fault detection filter for the lane-keeping control systems onboard vehicles used by California-PATH, USA in its automated highways program. We use a Luenberger structure for the fault detection filters and tune the observer gains based on an H/sub /spl infin//-based cost. Such a choice of cost was motivated by the need to explicitly incorporate frequency-domain-based performance objectives. The linear matrix inequality (LMI)-based formulation of an H/sub /spl infin// optimization problem of Luenberger state observers does not allow for the augmentation with dynamic performance weightings in the optimization objective, since it makes the problem a nonconvex optimization problem. We present an algorithm to locally solve the problem of the design of Luenberger state observers using H/sub /spl infin// optimization by transforming the problem into an H/sub /spl infin// static output feedback controller problem. Experimental results demonstrate the efficacy of the tuning methodology by comparing the fault detection performance of filters that use H/sub /spl infin// Luenberger observers versus those that use Kalman filters. Implementation issues of the observers are also discussed.     

Robust energy-to-peak filtering with improved LMI representations

The authors revisit the problem of robust energy-to-peak filtering for linear systems with parametric uncertainty residing in a polytope. Based on two results that appeared recently, they derive new L/sub 2/-L/sub /spl infin// performance criteria which allow the use of parameter-dependent Lyapunov functions for analysis and synthesis problems. Robust L/sub 2/-L/sub /spl infin// filters are then designed upon the new conditions and by means of the linear matrix inequality (LMI) technique, with the result that less conservativeness is achieved compared with earlier results that are based on a quadratic framework. Both continuous and discrete-time cases are considered and numerical examples illustrate the feasibility and advantage of the proposed designs.     

Robust filtering for discrete nonlinear fractional transformation systems

In this brief, we consider robust filtering problems for uncertain discrete-time systems. The uncertain plants under consideration possess nonlinear fractional transformation (NFT) representations which are a generalization of the classical linear fractional transformation (LFT) representations. The proposed NFT is more practical than the LFT, and moreover, it leads to substantial performance gains as well as computational savings. For this class of systems, we derive linear-matrix inequality characterizations for H/sub 2/, & H/sub /spl infin//, and mixed filtering problems. Our approach is finally validated through a number of examples.     

On discrete-time H/sub /spl infin// fixed-lag smoothing

The H/sub /spl infin// fixed-lag smoothing problem for discrete-time linear systems is considered. It is well known that such a problem can be reformulated as a filtering problem for a suitable augmented system. However, in order to check the solvability of the smoothing problem and compute the relevant gains, one must solve a Riccati equation involving the augmented system matrices, which is an approach that may be inefficient, especially for long lags. In this paper, efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H/sub /spl infin// filtering Riccati equation. In particular, this provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.