Delay-Dependent H∞ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays

This paper deals with the problems of delay-dependent robust H_infin control and filtering for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian delay systems are obtained by introducing some slack matrix variables. The conservatism caused by either model transformation or bounding techniques is reduced. Based on the proposed BRL, sufficient conditions for the solvability of the robust H_infin control and H_infin filtering problems are proposed, respectively. Dynamic output feedback controllers and full-order filters, which guarantee the resulting closed-loop system and the error system, respectively, to be stochastically stable and satisfy a prescribed H_infin performance level for all delays no larger than a given upper bound, are constructed. Numerical examples are provided to demonstrate the reduced conservatism of the proposed results in this paper.     

H∞ Finite Memory Controls for Linear Discrete-Time State-Space Models

In this brief, we propose a new type of output feedback control, called a H_infin finite memory control (HFMC), for discrete-time state-space systems. Some constraints, such as linearity, unbiasedness to the optimal state feedback control, and finite memory structure with respect to an input and an output are required in advance. Among the controls needed with these requirements, we choose the HFMC to optimize the H_infin performance criterion. The HFMC is obtained by solving the linear matrix inequality problem with a parameterization of a linear equality constraint. We show through simulation that the HFMC is more robust against uncertainties, and is faster in convergence than existing H_infin output feedback controls     

Dual H∞ Algorithms for Signal Processing— Application to Speech Enhancement

This paper deals with the joint signal and parameter estimation for linear state-space models. An efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual Kalman filters. In that case, the driving process and the observation noise in the state-space representation for each filter must be white with known variances. These conditions, however, are too strong to be always satisfied in real cases. To relax them, we propose a new approach based on two dual H_infin filters. Once a new observation of the disturbed signal is available, the first H_infin algorithm uses the latest estimated parameters to estimate the signal, while the second H_infin algorithm uses the estimated signal to update the parameters. In addition, as the H_infin filter behavior depends on the choice of various weights, we present a way to recursively tune them. This approach is then studied in the following cases: (1) consistent estimation of the AR parameters from noisy observations and (2) speech enhancement, where no a priori model of the additive noise is required for the proposed approach. In each case, a comparative study with existing methods is carried out to analyze the relevance of our solution.     

Robust and reduced-order filtering: new LMI-based characterizationsand methods

This paper addresses several challenging problems of robust filtering. We derive new linear matrix inequality (LMI) characterizations of minimum variance or H₂ performance and demonstrate that they allow the use of parameter-dependent Lyapunov functions while preserving tractability of the problem. The resulting conditions are less conservative than earlier techniques, which are restricted to fixed (not parameter-dependent) Lyapunov functions. The remainder of the paper discusses reduced-order filter problems. New LMI-based nonconvex optimization formulations are introduced for the existence of reduced-order filters, and several efficient optimization algorithms of local and global optimization are proposed. Nontrivial and less conservative relaxation techniques are presented as well. The viability and efficiency of the proposed approaches are then illustrated through computational experiments and comparisons with existing methods     

Robust ℋ∞ filtering for uncertaindiscrete-time state-delayed systems

This paper addresses the problem of robust ℋ_∞ filtering for linear discrete-time systems subject to parameter uncertainties in the system state-space model and with multiple time delays in the state variables. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. A methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed ℋ_∞ performance for the filtering error, irrespective of the uncertainty and the time delays. The proposed design is given in terms of linear matrix inequalities, which has the advantage in that it can be implemented numerically very efficiently     

A New Parameter-Dependent Approach to Robust Energy-to-Peak Filter Design

This paper presents a new parameter-dependent approach to the design of robust energy-to-peak filters for linear uncertain systems. Given a system containing polytopic parameter uncertainties, our purpose is to design a robust filter such that the filtering error system is asymptotically stable with a guaranteed L₂-L_∞ disturbance attenuation level γ. This problem is solved by introducing new energy-to-peak performance characterizations, and by utilizing an idea of structured parameter-dependent matrices. New sufficient conditions are obtained for the existence of desired filters in terms of linear matrix inequalities, which can be easily tested by using standard numerical software. If these conditions are satisfied, a desired filter can be readily constructed. Both continuous- and discrete-time systems are considered, and the effectiveness and advantages of the proposed filter design methods are shown via two numerical examples.     

A delay-dependent approach to robust H/sub /spl infin// filtering for uncertain discrete-time state-delayed systems

A delay-dependent approach to robust H/sub /spl infin// filtering is proposed for linear discrete-time uncertain systems with multiple delays in the state. The uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed H/sub /spl infin// noise attenuation level. The proposed filter design methodology incorporates some recently appeared results, such as Moon's new version of the upper bound for the inner product of two vectors and de Oliveira's idea of parameter-dependent stability, which greatly reduce the overdesign introduced in the derivation process. In addition to the full-order filtering problem, the challenging reduced-order case is also addressed by using different linearization procedures. Both full- and reduced-order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies.     

A Generalized Parameter-Dependent Approach to Robust H ∞ Filtering of Stochastic Systems

This paper is concerned with the problem of robust H _∞ filtering for discrete-time stochastic systems with state-dependent stochastic noises and deterministic polytopic parameter uncertainties. We utilize the polynomial parameter-dependent approach to solve the robust H _∞ filtering problem, and the proposed approach includes results in the quadratic framework that entail fixed matrices for the entire uncertain domain and results in the linearly parameter-dependent framework that use linear convex combinations of matrices as special cases. New linear matrix inequality (LMI) conditions obtained for the existence of admissible filters are developed based on homogeneous polynomial parameter-dependent matrices of arbitrary degree. As the degree grows, a test of increasing precision is obtained, providing less conservative filter designs. A numerical example is provided to illustrate the effectiveness and advantages of the filter design methods proposed in this paper. This work was supported by HKU CRCG 200611159157, the National Nature Science Foundation of China (60504008), The Research Fund for the Doctoral Programme of Higher Education of China (20070213084), the Fok Ying Tung Education Foundation (111064), and the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University), Ministry of Education of China.     

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 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.     

H/sub /spl infin// mode reduction for two-dimensional discrete state-delayed systems

The problem of H_infin model reduction for two-dimensional (2-D) discrete systems with delay in state is considered. The mathematical model of 2-D systems is established on the basis of the well-known Fornasini-Marchesini local state-space. First, conditions are established to guarantee the asymptotic stability and a prescribed noise attenuation level in the H_infin sense for the underlying system. For a given stable system, attention is focused on the construction of a reduced-order model, which approximates the original system well in an H_infin norm sense. Sufficient conditions are proposed for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearisation method is exploited to cast them into sequential minimisation problems subject to LMI constraints, which can be readily solved using standard numerical software. These obtained results are further extended to more general cases whose system states contain multiple delays. Two numerical examples are provided to demonstrate the effectiveness of the proposed techniques     

A Fault-Tolerant Manipulator Robot Based on ${{cal H}}_2$, ${{cal H}}_{infty }$, and Mixed ${{cal H}}_2/{{cal H}}_{infty }$ Markovian Controls

This paper develops a Markovian jump model to describe the fault occurrences in a manipulator robot of three joints. This model includes the changes of operation points and the probability that a fault occurs in an actuator. After a fault, the robot works as a manipulator with free joints. Based on the developed model, a comparative study among three Markovian controllers, H₂, H_infin, and mixed H₂/H_infin is presented, applied in an actual manipulator robot subject to one and two consecutive faults.     

Convex Optimization Approaches to Robust ℒ1 Fixed-Order Filtering for Polytopic Systems with Multiple Delays

This paper investigates the robust ℒ₁ fixed-order filtering problem for continuous polytopic systems with multiple state delays. Attention is focused on the design of robust full-order and reduced-order filters that guarantee the filtering error system to be asymptotically stable and satisfy the worst case peak-to-peak gain of the filtering error system for all admissible uncertainties and time delays. In particular, we concentrate on the delay-dependent case, and the peak-to-peak performance criterion is first established for polytopic systems with multiple state delays. Two different convex optimization approaches are proposed to solve this problem. One is the parameter-dependent Lyapunov approach in which the filter is not only dependent on the parameters (residing in a polytope), but also the Lyapunov matrices are different over the entire polytope domain. The other is the quadratic stability approach which obtains an admissible filter in the quadratic framework. Computational algorithms in terms of linear matrix inequalities (LMIs) are provided. It is shown that the parameter-dependent Lyapunov approach turns out to be less conservative than the quadratic stability approach, but the quadratic stability approach is computationally less demanding. Two numerical examples are presented to illustrate the proposed theory. This work was partially supported by RGC HKU 7028/04P, the Natural Science Foundation of Heilongjiang Province under Grant F200504, and the Scientific and Technical Research Project of the Education Department of Heilongjiang Province under Grant 10551013.     

A novel Hα control strategy for design of a robust dynamic routing algorithm in traffic networks

In this paper novel centralized and decentralized routing control strategies based on minimization of the worst-case queuing length are proposed. The centralized routing problem is formulated as an H_infin optimal control problem to achieve a robust routing performance in presence of multiple and unknown fast time-varying network delays. Unlike similar previous work in the literature the delays in the queuing model are assumed to be unknown and time-varying. A Linear Matrix Inequality (LMI) constraint is obtained to design a delay-dependent H_infin controller. The physical constraints that are present in the network are then expressed as LMI feasibility conditions. Our proposed centralized routing scheme is then reformulated in a decentralized frame work. This modification yields an algorithm that obtains the "fastest route", increases the robustness against multiple unknown time-varying delays, and enhances the scalability of the algorithm to large scale traffic networks. Simulation results are presented to illustrate and demonstrate the effectiveness and capabilities of our proposed novel dynamic routing strategies.     

Sensorless speed measurement using current harmonic spectralestimation in induction machine drives

This paper proposes a sensorless speed measurement scheme that improves the performance of transducerless induction machine drives, especially for low-frequency operation. Speed-related harmonics that arise from rotor slotting and eccentricity are analyzed using digital signal processing. These current harmonics exist at any nonzero speed and are independent of time-varying parameters, such as stator winding resistance. A spectral estimation technique combines multiple current harmonics to determine the rotor speed with more accuracy and less sensitivity to noise than analog filtering methods or the fast Fourier transform. An on-line initialization routine determines machine-specific parameters required for slot harmonic calculations. This speed detector, which has been verified at frequencies as low as 1 Hz, can provide robust, parameter-independent information for parameter tuning or as an input to a sensorless flux observer for a field-oriented drive. The performance of the algorithm is demonstrated over a wide range of inverter frequencies and load conditions     

Adaptive H∞ channel equalization for wirelesspersonal communications

In this paper, a new adaptive H_∞ filtering algorithm is developed to recursively update the tap-coefficient vector of a decision feedback equalizer (DFE) in order to adaptively equalize the time-variant dispersive fading channel of a high-rate indoor wireless personal communication system. Different from conventional L ₂ (such as the recursive least squares (RLS)) filtering algorithms which minimize the squared equalization error, the adaptive H _∞ filtering algorithm is a worst case optimization. It minimizes the effect of the worst disturbances (including input noise and modeling error) on the equalization error. Hence, the DFE with the adaptive H_∞ filtering algorithm is more robust to the disturbances than that with the RLS algorithm. Computer simulation demonstrates that better transmission performance can be achieved using the adaptive H_∞ algorithm when the received signal-to-noise ratio (SNR) is larger than 20 dB     

Robust H/sub 2/ filtering for a class of systems with stochastic nonlinearities

This paper addresses the robust H/sub 2/ filtering problem for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities described by statistical means in this paper comprise some well-studied classes of nonlinearities in the literature. A technique is developed to tackle the matrix trace terms resulting from the nonlinearities, and the well-known S-procedure technique is adopted to cope with the uncertainties. A unified framework is established to solve the addressed robust H/sub 2/ filtering problem by using a linear matrix inequality approach. A numerical example is provided to illustrate the usefulness of the proposed method.     

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.