H∞ filter design for a class of nonlinear discrete-time singular systems

This paper deals with the H_∞ filter design problem for a class of discrete-time Lipschitz nonlinear singular systems. The approach is based on the parameterisation of the obtained algebraic constraints from the estimation errors. Sufficient conditions for the existence of the filters which guarantee stability and the worst case filter error energy over all bounded energy disturbances is minimised are given. The method also unifies the design for the full-order, reduced-order, minimal-order filters for discrete- time systems. The presented results are less conservative than those existing in the literature, this is due to the introduction of new slack variables. Application to systems with unknown input is presented via a numerical example.     

Quantised H ∞ filter design for discrete-time systems

This article is concerned with the quantised H _∞ filtering problem for discrete-time systems. The quantiser considered here is dynamic and composed of a dynamic scaling and a static quantiser. Motivated by practical transmission channels requirements, the static quantiser ranges are fully considered in this article. A quantised H _∞ filter design strategy is proposed, taking quantiser errors into account, where a convex optimisation method is developed to minimise static quantiser ranges with meeting H _∞ performance requirement for quantised augmented systems. A numerical example is given to illustrate the effectiveness of the proposed filter design method.     

H∞ filter design for nonlinear systems with quantised measurements in finite frequency domain

This paper deals with the problem of finite frequency (FF) H_∞ full-order fuzzy filter design for nonlinear discrete-time systems with quantised measurements, described by Takagi–Sugeno models. The measured signals are assumed to be quantised with a logarithmic quantiser. Using a fuzzy-basis-dependent Lyapunov function, the finite frequency ?₂ gain definition, the generalised S-procedure, and Finsler's lemma, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H_∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. With the aid of Finsler's lemma, a large number of slack variables are introduced to the design conditions, which provides extra degrees of freedom in optimising the guaranteed H_∞ performance. This directly leads to performance improvement and reduction of conservatism. Finally, we give a simulation example to demonstrate the efficiency of the proposed design method, and we show that a lower H_∞ attenuation level can be obtained by our developed approach in comparison with another result in the literature.     

Fuzzy robust H ∞ filter design for nonlinear discrete-time systems with interval time delays

This article deals with the problem of H _∞ filter design for nonlinear discrete-time systems with norm-bounded parameter uncertainties and time-varying delays. A new Lyapunov function and free-weighting matrix method are used for filtering design, consequently, a delay-dependent design method is first proposed in terms of linear matrix inequalities, which produces a less conservative result. Finally, numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.     

Robust H ∞ filter design for affine fuzzy systems

This paper investigates the problem of robust H _∞ filtering for nonlinear systems, which are described by affine fuzzy parts with norm-bounded uncertainties. The system outputs have been chosen as premise variables, which can guarantee the plant and the filter always switch to the same region. By using a piecewise Lyapunov function and adding slack matrix variables, a fuzzy-basis-dependent H _∞ filter design method is obtained in the formulation of linear matrix inequalities (LMIs), which can be efficiently solved numerically. Compared with the existing results, the proposed method needs less LMI constraints and leads to less conservatism. Finally, numerical examples illustrate the effectiveness of the new results.     

Robust H2/H∞ global linearization filter design for nonlinear stochastic time-varying delay systems

One can design a robust H_∞ filter for a general nonlinear stochastic system with external disturbance by solving a second-order nonlinear stochastic partial Hamilton-Jacobi inequality (HJI), which is difficult to be solved. In this paper, the robust mixed H₂/H_∞ globally linearized filter design problem is investigated for a general nonlinear stochastic time-varying delay system with external disturbance, where the state is governed by a stochastic Itô-type equation. Based on a globally linearized model, a stochastic bounded real lemma is established by the Lyapunov–Krasovskii functional theory, and the robust H_∞ globally linearized filter is designed by solving the simultaneous linear matrix inequalities instead of solving an HJI. For a given attenuation level, the H₂ globally linearized filtering problem with the worst case disturbance in the H_∞ filter case is known as the mixed H₂/H_∞ globally linearized filtering problem, which can be formulated as a linear programming problem with simultaneous LMI constraints. Therefore, this method is applicable for state estimation in nonlinear stochastic time-varying delay systems with unknown exogenous disturbance when state variables are unavailable. A simulation example is provided to illustrate the effectiveness of the proposed method.     

Robust H ∞ filter design for time-delay systems with saturation

This paper investigates the H∞ filtering problem for a class of linear continuous-time systems with both time delay and saturation. Such systems have time delay in their state equations and saturation in their output equations, and their process and measurement noises have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the linear matrix inequalities (LMIs) technique, a generalized dynamic filter architecture is proposed, and a filter design method is developed. The linear H∞ filter designed by the method can guarantee the H∞ performance. The parameters of the designed filter can be obtained by solving a kind of LMI. An illustrative example shows that the design method proposed in this paper is very effective.     

H ∞ filter design for continuous-time systems with quantised signals

This article studies the quantised H _∞ filtering problem for continuous-time systems with a type of dynamic quantisers, which are conjuncted with static quantisers via dynamic scalings. The static quantiser ranges are fully considered here for practical transmission channels requirements. A quantised H _∞ filter design strategy is proposed, where a convex optimisation method is developed to minimise static quantiser ranges. The resulting design guarantees that the quantised augmented system is asymptotically stable and with a prescribed H _∞ performance bound. The effectiveness of the proposed filter design method is demonstrated by a numerical example.     

Control design approaches for nonlinear systems using multiple models

It is difficult to realize control for some complex nonlinear systems operated in different operating regions. Based on developing local models for different operating regions of the process, a novel algorithm using multiple models is proposed. It utilizes dynamic model bank to establish multiple local models, and their membership functions are defined according to respective regions. Then the nonlinear system is approximated to a weighted combination of the local models. The stability of the nonlinear system is proven. Finally, simulations are given to demonstrate the validity of the proposed method.     

State-feedback ℋ∞ control for stochastic time-delay nonlinear systems with state and disturbance-dependent noise

This article focuses on the state-feedback ?_∞ control problem for the stochastic nonlinear systems with state and disturbance-dependent noise and time-varying state delays. Based on the maxmin optimisation approach, both the delay-independent and the delay-dependent Hamilton–Jacobi-inequalities (HJIs) are developed for synthesising the state-feedback ?_∞ controller for a general type of stochastic nonlinear systems. It is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level. For a class of stochastic affine nonlinear systems, the delay-independent as well as delay-dependent matrix-valued inequalities are proposed; the resulting control system satisfies global asymptotic stability in the mean-square sense and the required disturbance attenuation level. By modelling the nonlinearities as uncertainties in corresponding stochastic time-delay systems, the sufficient conditions in terms of a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) are derived to facilitate the design of the state-feedback ?_∞ controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.     

New results on H ∞ filter design for nonlinear systems with time-delay through a T-S fuzzy model approach

H _∞ filter design for nonlinear systems with time-delay via a T-S fuzzy model approach is investigated based on a piecewise analysis method. Two cases of time-varying delays are fully considered: one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with delay-derivative bounded by a constant. Based on a piecewise analysis method, the variation interval of the time delay is first divided into several subintervals, then the convexity property of the matrix inequality and the free weighting matrix method are fully used in this article. Some novel delay-dependent H _∞ filtering criteria are expressed as a set of linear matrix inequalities, which can lead to much less conservative analysis results. Finally, a numerical example is given to illustrate that the results in this article are more effective and less conservative than some existing ones.     

H ∞ switching filter design for LPV systems in finite frequency domain

This article studies the problem of finite frequency H _∞ filter design for switching linear parameter varying (LPV) systems with disturbance frequency affected by system parameters. A set of switching filters are designed, each suitable for a specific parameter subregion and a specific finite frequency performance index. A hysteresis switching logic is adopted, and the design problem is finally formulated into linear matrix inequality (LMI) which can be solved efficiently with LMI Control Toolbox. A numerical example is given to illustrate the effectiveness of the proposed method.     

Adaptive robust H ∞ filter design for linear systems with time-varying uncertainty

This article studies the problem of designing robust H _∞ filters for linear uncertain systems. The uncertainty parameters are assumed to be time-varying, unknown, but bounded, which appear affinely in the matrices of system models. An adaptive mechanism is introduced to construct novel filters with variable gains, which can reduce the conservativeness of the traditional robust H _∞ filters. The proposed adaptive filter design conditions are given in terms of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed strategy.     

H ∞ filter design for discrete delay systems: a new parameter-dependent approach

This article revisits the problem of H _∞ filtering for discrete-time systems with a time-varying delay in the state and parameter uncertainties residing in a polytope. By utilising the polynomially parameter-dependent idea, a new filter design procedure is proposed, which formulates the existence of admissible robust H _∞ filters into a set of linear matrix inequalities. These conditions are developed based on homogeneous polynomially parameter-dependent matrices of an arbitrary degree. As the degree grows, test of increasing precision is obtained providing less conservative filter designs. It is established that the results in the quadratic framework (that entail fixed matrices for the entire uncertainty domain), and the linearly parameter-dependent framework (that use linear convex combinations of matrices) are special cases of the proposed conditions for the zeroth degree and the first degree, respectively. Moreover, in addition to parameter dependence, the obtained conditions are also dependent on both the upper and lower bounds of the delay, which is obtained by using advanced techniques for achieving delay dependence. Several numerical examples are given to illustrate the effectiveness and advantage of the proposed filter design methods.     

Robust H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It^o stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.