H/sub /spl infin// fuzzy output feedback control design for nonlinear systems: an LMI approach

Addresses the problem of stabilizing a class of nonlinear systems by using an H/sub /spl infin// fuzzy output feedback controller. First, a class of nonlinear systems is approximated by a Takagi-Sugeno (TS) fuzzy model. Then, based on a well-known Lyapunov functional approach, we develop a technique for designing an H/sub /spl infin// fuzzy output feedback control law which guarantees the L/sub 2/ gain from an exogenous input to a regulated output is less or equal to a prescribed value. A design algorithm for constructing an H/sub /spl infin// fuzzy output feedback controller is given. In contrast to the existing results, the premise variables of the H/sub /spl infin// fuzzy output feedback controller are not necessarily to be the same as the premise variables of the TS fuzzy model of the plant. A numerical simulation example is presented to illustrate the theory development.     

Global H/sub /spl infin// controllers for a class of nonlinear systems

In this note, the problem of state feedback H/sub /spl infin// control for a class of nonlinear systems is considered. The class under study is a generalization of the well-known Lur'e systems. The H/sub /spl infin// problem is addressed via a class of storage functions of the Lur'e-Postnikov type whose integral term is parameterized by a nonlinear scalar function. The related H/sub /spl infin// controllers consist of a linear term, which is designed for the underlying linearized system, plus a nonlinear term which depends on the nonlinear function. A simple geometrical criterion is provided for the characterization of the set of controllers which ensure a given level of L/sub 2/-performance globally. Some guidelines for an effective design of the controller within this set are discussed via two examples.     

Robust H/sub /spl infin// control for uncertain discrete-time-delay fuzzy systems via output feedback controllers

This work investigates the problem of robust output feedback H/sub /spl infin// control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi-Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H/sub /spl infin// norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H/sub /spl infin// control for a class of uncertain nonlinear discrete delay systems.     

Robust H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization designs of nonlinear communication systems: fuzzy interpolation approach

Generally, it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises. In this paper, we propose the H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization/detection of nonlinear channels using fuzzy interpolation and linear matrix inequality (LMI) techniques. First, the signal transmission system is described as a state-space model and the input signal is embedded in the state vector such that the signal reconstruction (estimation) design becomes a nonlinear state estimation problem. Then, the Takagi-Sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions. Since the statistics of noises are unknown, the fuzzy H/sub /spl infin// equalizer is proposed to treat the state estimation problem from the worst case (robust) point of view. When the statistics of noises are uncertain but with some nominal (or average) information available, the mixed H/sub 2//H/sub /spl infin// equalizer is employed to take the advantage of both H/sub 2/ optimal performance with nominal statistics of noises and the H/sub /spl infin// robustness performance against the statistical uncertainty of noises. Using the LMI approach, the fuzzy H/sub 2//H/sub /spl infin// equalizer/detector design problem is characterized as an eigenvalue problem (EVP). The EVP can be solved efficiently with convex optimization techniques.     

Sufficient LMI conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems

In this note, sufficient conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems are proposed via linear matrix inequalities (LMIs). In order to reduce conservatism existing in earlier LMI methods, auxiliary slack variables with structure are employed. It is shown that degree of freedoms by the introduction of auxiliary slack variables lead to more flexibility in obtaining an approximate solution of H/sub /spl infin// output feedback stabilization problems. Consequently, the proposed method can yield a less conservative result than earlier LMI methods. In particular, typical output feedback control problems, such as decentralized H/sub /spl infin// output feedback control and simultaneous H/sub /spl infin// output feedback control, can be more efficiently solved. Numerical examples are included to illustrate the advantages of the proposed LMI method.     

Fuzzy H/sub /spl infin// output feedback control design for singularly perturbed systems with pole placement constraints: an LMI approach

This paper examines the problem of designing an H/sub /spl infin// output feedback controller with pole placement constraints for singular perturbed Takagi-Sugeno (TS) fuzzy models. We propose a fuzzy H/sub /spl infin// output feedback controller that not only guarantees the /spl Lscr//sub 2/-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, but also ensures closed-loop poles of each subsystem are in a prespecified linear matrix inequality (LMI) region. In order to alleviate the numerical stiffness caused by the singular perturbation /spl epsiv/, the design technique is formulated in terms of a family of /spl epsiv/-independent linear matrix inequalities. The proposed approach can be applied both standard and nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.     

Nonlinear H/sub /spl infin// controllers for electromagnetic suspension systems

This note presents a unified framework to derive nonlinear H/sub /spl infin// state and output feedback controllers for magnetically levitated (Maglev) vehicles with controlled dc electromagnets, referred to as electromagnetic suspension systems. The theoretical exposition, based on the Taylor series expansion solution to the Hamilton-Jacobi-Isaacs inequality, is followed by an assessment of some of the practical issues in realizing the nonlinear controllers with a digital signal processor and embedded hardware. A select set of experimental results from a single-degree-of-freedom suspension system is included to highlight the effectiveness of the proposed nonlinear stateand output-feedback H/sub /spl infin// controllers to suppress guideway-induced disturbances.     

Robust H/sub /spl infin// static output feedback control of fuzzy systems: an ILMI approach

This paper examines the problem of robust H/sub /spl infin// static output feedback control of a Takagi-Sugeno fuzzy system. The proposed robust H/sub /spl infin// static output feedback controller guarantees the L/sub 2/ gain of the mapping from the exogenous disturbances to the regulated output to be less than or equal to a prescribed level. The existence of a robust H/sub /spl infin// static output feedback control is given in terms of the solvability of bilinear matrix inequalities. An iterative algorithm based on the linear matrix inequality is developed to compute robust H/sub /spl infin// static output feedback gains. To reduce the conservatism of the design, the structural information of membership function characteristics is incorporated. A numerical example is used to illustrate the validity of the design methodologies.     

Delay-dependent robust H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering for a class of uncertain nonlinear time-delay systems

This note presents delay-dependent robust H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filter designs for a class of nonlinear systems with multiple time-varying delays in the state and parameter uncertainties residing in a polytope. The nonlinearities are assumed to satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H/sub /spl infin// or L/sub 2/-L/sub /spl infin// sense. The admissible 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.     

H/sub /spl infin//-optimal preview controller and its performance limit

In this note, H/sub /spl infin//-optimal preview control problem is discussed. The problem is reduced to finite-dimensional H/sub /spl infin// problem, whose solution algorithm is well known. Also, the performance limit by the optimal controller is clearly explained.     

Robust H/sub /spl infin// control for fuzzy systems with Frobenius norm-bounded uncertainties

In this paper, we investigate the problem of robust H/sub /spl infin// performance and stabilization for a class of uncertain fuzzy systems with Frobenius norm-bounded parameter uncertainties in all system matrices. Both continuous- and discrete-time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems. Unlike the bounded real lemma in the linear theory of robust H/sub /spl infin// control where necessary and sufficient conditions were obtained, only sufficient condition based on Lyapunov method is shown. Furthermore, connection between robust H/sub /spl infin// problems involving uncertainty and standard uncertainty-free H/sub /spl infin// problems is established via matrix algebra. As for controller synthesis, a state feedback fuzzy control law is designed via relaxed linear matrix inequality (LMI) formulations.     

An exact solution to general SISO mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// problems via convex optimization

The mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// control problem can be motivated as a nominal LQG optimal control problem, subject to robust stability constraints, expressed in the form of an /spl Hscr//sub /spl infin// norm bound. A related modified problem consisting on minimizing an upper bound of the /spl Hscr//sub 2/ cost subject to /spl Hscr//sub /spl infin// constraints was introduced by Bernstein-Haddad (1989). Although there presently exist efficient methods to solve this modified problem, the original problem remains, to a large extent, still open. In this paper we propose a method for solving general discrete-time SISO /spl Hscr//sub 2///spl Hscr//sub /spl infin// problems. This method involves solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and an unconstrained Nehari approximation problem.<>     

Robust nonlinear control associating robust feedback linearization and H/sub /spl infin// control

In this note, a robust nonlinear controller for a nonlinear system subject to model uncertainties is proposed. Such a controller associates a "robust feedback linearization" with a robust linear H/sub /spl infin// controller. The robust feedback linearization exactly transforms the nonlinear system into a linear system equal to the linear approximation of the original nonlinear system around a nominal operating point. The robustness of the resulting overall nonlinear controller is proved by theoretical arguments and illustrated through an application example, the control of a magnetic bearing system.     

Stochastic H/sub 2//H/sub /spl infin// control with state-dependent noise

This paper discusses the stochastic H/sub 2//H/sub /spl infin// control problem with state-dependent noise. By means of the stabilization, exact observability and stochastic detectability of stochastic systems, the infinite horizon stochastic H/sub 2//H/sub /spl infin// control design is developed. For the finite horizon H/sub 2//H/sub /spl infin// control problem, our results generalize the corresponding deterministic ones to the stochastic models. Finally, the observer-based suboptimal stochastic H/sub 2//H/sub /spl infin// control is discussed in which the state variables cannot be measured directly, and a feasible design algorithm is proposed.     

Constantly scaled H/sub /spl infin// control problems for pseudofull information problems

This paper proposes a class of the constantly scaled H/sub /spl infin// control problem, where the class is characterized by an assumption also proposed in this paper. In general, the scaled H/sub /spl infin// control problem leads to nonconvex solvability conditions. On the other hand, for the problems in the proposed class, we show that a convex but sufficient solvability condition can be given. Moreover, the convexity of the state feedback and the full information problems can be regarded as the extreme cases of the sufficient condition. This fact motivates us to call the assumption the pseudofull information condition.     

Robust sampled-data H/sub /spl infin// control of linear singularly perturbed systems

State-feedback H/sub /spl infin// control problem for linear singularly perturbed systems with norm-bounded uncertainties is studied. The fast variables are sampled with fast rates, while for the slow variables both cases of slow and of fast sampling are considered. The recent "input delay" approach to sampled-data control is applied, where the closed-loop system is represented as a continuous one with time-varying input delay. Linear matrix inequalities (LMIs) for solution of H/sub /spl infin// control problem are derived via input-output approach to stability and L/sub 2/-gain analysis of time-delay systems. A numerical example illustrates the efficiency of the method.     

An innovation approach to H/sub /spl infin// fixed-lag smoothing for continuous time-varying systems

This note studies the finite horizon H/sub /spl infin// fixed-lag smoothing problem for linear continuous time-varying systems. A technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H/sub /spl infin// fixed-lag smoother. The condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two Riccati differential equations (RDEs), one standard H/sub /spl infin// filtering RDE and one H/sub 2/ type of RDE. Examples demonstrate the proposed H/sub /spl infin// fixed-lag smoother design and the fact that the existence of an H/sub /spl infin// smoother does not depend on the solvability of H/sub /spl infin// filtering.     

Fault detection in a mixed H/sub 2//H/sub /spl infin// setting

In this note, we study the problem of fault detection in linear time-invariant (LTI) systems which are simultaneously effected by two classes of unknown inputs: Noises having fixed spectral densities and unknown finite energy disturbances. This problem is formulated as a mixed H/sub 2//H/sub /spl infin// filtering problem. Necessary and sufficient conditions for local optimality are presented. Moreover, it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality (LMI) constrains. A numerical example is given to illustrate the advantage of the mixed H/sub 2//H/sub /spl infin// approach as compared to existing techniques which are based on optimization of H/sub 2/ and H/sub /spl infin// criteria.     

A reduced order observer based controller design for H/sub /spl infin//-optimization

In this note the H/sub /spl infin// control problem with measurement feedback is investigated. It is well-known that for this problem, in general, we need controllers of the same dynamic order as the given system. However, in the case that some entries of the measurement vector are not noise-corrupted, we show that one can find dynamic compensators of a lower dynamical order. Note that this implies that the standard assumptions on the direct feedthrough matrices, as made in most papers on H/sub /spl infin// control, are not satisfied. Our result can be derived by using reduced order observer based controllers.<>