An LMI approach to robust H∞ filtering for uncertain systems with time-varying distributed delays

In this paper, the problem of robust H_∞ filtering for uncertain systems with time-varying distributed delays is considered. The uncertainties under discussion are time varying but norm bounded. Based on the Lyapunov stability theory, sufficient condition for the existence of full order H_∞ filters is proposed by linear matrix inequality (LMI) approach such that the filtering error system is asymptotically sable and satisfies a prescribed attenuation level of noise. A numerical example is given to demonstrate the availability of the proposed method.     

H∞ filtering for nonlinear systems via neural networks

A novel H_∞ filter design methodology has been presented for a general class of nonlinear systems. Different from existing nonlinear filtering design, the nonlinearities are approximated using neural networks, and then are modeled based on linear difference inclusions, which makes the structure of the desired filter simpler and parameter turning easier and has the advantages of guaranteed stability, numeral robustness, bounded estimation accuracy. A unified framework is established to solve the addressed H_∞ filtering problem by exploiting linear matrix inequality (LMI) approach. A numerical example shows that the filtering error systems will work well against bounded error between a nonlinear dynamical system and a multilayer neural network.     

Delay-dependent H∞ filtering of uncertain Markovian jump delay systems via delay-partitioning approach

In this paper, the problem of _H∞$H_{\infty }$ filtering of uncertain time-delay systems with Markovian jumping parameters is considered. Firstly, by utilizing the delay-partitioning idea, an augmented mode-dependent Lyapunov functional is employed to analyze the stochastic stability and _H∞$H_{\infty }$ performance of the resulting filtering error systems. It is noted that the derived performance analysis results are less conservative than the recent ones in the literature. Secondly, based on the criteria obtained, a desired filter can be constructed by introducing a given nonsingular matrix and a scalar. Numerical examples are given to illustrate the effectiveness of the proposed approach.     

Non-fragile robust H∞ control for uncertain discrete-time singular systems with time-varying delays

In this paper, the problem of delay-dependent non-fragile robust H∞$H\infty$ control for a class of discrete-time singular systems with state-delay and parameter uncertainties is investigated. Based on singular value decomposition approach, a delay-dependent sufficient condition for the H∞$H\infty$ control problem for a class of discrete-time singular systems is proposed by constructing generalized Lyapunov–Krasovskii function and a new difference inequality. A memoryless state feedback controller under controller gain perturbations is designed, which guarantees that, for all admissible uncertainties, the resultant closed-loop system is regular, causal, and stable with an H∞$H\infty$ norm bound constraint. Numerical examples in the last will show that our results have the better performance in conservativeness than some results reported in the literature.     

Central suboptimal H∞ filtering for nonlinear polynomial systems with multiplicative noise

This paper presents the central finite-dimensional H_∞ filter for nonlinear polynomial systems with multiplicative noise, that is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H_∞ filtering problem to the corresponding optimal H₂ filtering problem, using the technique proposed in [1]. The paper presents the central suboptimal H_∞ filter for the general case of nonlinear polynomial systems with multiplicative noise, based on the optimal H₂ filter given in [31]. The central suboptimal H_∞ filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H_∞ filters available for polynomial systems with state-independent noise and the corresponding linearized system.     

New robust delay-dependent stability and H∞ analysis for uncertain Markovian jump systems with time-varying delays

This paper deals with the problems of robust delay-dependent stability and H_∞ analysis for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, an improved delay-range-dependent stability condition for Markovian jump systems is proposed by constructing a novel Lyapunov-Krasovskii functional with the idea of partitioning the time delay, and a sufficient condition is derived from the H_∞ performance. Numerical examples are provided to demonstrate efficiency and reduced conservatism of the results in this paper.     

H∞ optimization-based decentralized control of linear interconnected systems with nonlinear interconnections

The focus of this paper is on the design of a _H∞$H_{\infty }$ decentralized observation and control approach for a class of nonlinear disturbed interconnected systems. The proposed scheme is formulated as an optimization problem in terms of linear matrix inequality (LMI) to compute the robust observation and control gain matrices simultaneously, to maximize the bounds on the nonlinearity which the system can tolerate without going unstable, to improve the performance of the proposed control strategy by minimizing the _H∞$H_{\infty }$ criterion and to ensure the stability of the closed loop system in the Lyapunov framework despite the exogenous disturbances applied to the subsystems. A simulation is provided on a 3-machine power system, which generators are strongly nonlinear interconnected, to show the efficiency of the designed approach.     

A Markovian system approach to distributed H∞ filtering for sensor networks with stochastic sampling

This paper is concerned with the distributed H_∞ filtering problem for a class of sensor networks with stochastic sampling. System measurements are collected through a sensor network stochastically and the phenomena such as random measurement missing and quantization are also considered. Firstly, the stochastic sampling process of the sensor network is modeled as a discrete-time Markovian system. Then, the logarithmic quantization effect is transformed into the parameter uncertainty of the filtering system, and a set of binary variables is introduced to model the random measurement missing phenomenon. Finally, the resulting augmented system is modeled as an uncertain Markovian system with multiple random variables. Based on the Lyapunov stability theory and the stochastic system analysis method, a sufficient condition is obtained such that the augmented system is stochastically stable and achieves an average H_∞ performance level γ; the design procedure of the optimal distributed filter is also provided. A numerical example is given to demonstrate the effectiveness of the proposed results.     

Quantized H∞ output feedback control for linear discrete-time systems

This paper investigates the robust _H∞$H_{\infty }$ dynamic output feedback control problem for networked control systems (NCSs) with quantized measurements. The measurement losses of the communicated information are considered in an unreliable communication channel. The robust _H∞$H_{\infty }$ dynamic output feedback controllers are designed to handle the measurement losses and mitigate the quantization effects such that the resultant closed-loop NCS is mean-square stochastically stable with a prescribed _H∞$H_{\infty }$ disturbance attenuation performance. The controller existence conditions can be derived in terms of linear matrix inequalities (LMIs). Finally, an example is provided to illustrate the effectiveness of the proposed approach.     

H∞ guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays

This paper investigates the H_∞ guaranteed cost control problem for mode-dependent time-delay jump systems with norm-bounded uncertain parameters. Both distributed delays and input delays appear in the system model. Based on a matrix inequality, a sufficient condition for the existence of robust H_∞ guaranteed cost controller is derived, which stabilizes the considered system and guarantees that both the H_∞ performance level and a cost function have upper bounds for all admissible uncertainties. By the cone complementary linearization approach, the desired state-feedback controller can be constructed. A numerical example is provided to show the effectiveness of the proposed theoretical results.     

Nonlinear H∞ feedback control with integrator for polynomial discrete-time systems

This paper investigates the problem of designing a nonlinear _H∞$H_{\infty }$ feedback controller for polynomial discrete-time systems with and without polytopic uncertainties. The objective is to design a controller such that the ratio between the energy of the regulated outputs and the energy of the exogenous disturbance/inputs is minimized or guaranteed to be less or equal to a prescribed value. It is well known that the state dependant or parameter dependant Lyapunov function is always chosen for synthesizing polynomial discrete-time systems. This leads the solution to be nonconvex because the Lyapunov function and the controller matrix are coupled and therefore cannot be solved by semidefinite programming (SDP). Hence, in this paper, an integrator is proposed to be incorporated into the controller structure. In doing so, the coupling of Lyapunov function and controller matrix can be eliminated effectively. This somehow simplifies the numerical solution of the problem. Then, by using SOS decomposition approach, sufficient conditions for the existence of the proposed controller are provided in terms of solvability of the state-dependent linear matrix inequalities (SDLMIs) which can be solved by SDP. A tunnel diode circuit is used to demonstrate the effectiveness of this integrator approach.     

Non-fragile H∞ filter design with sparse structure for linear discrete-time systems

This paper presents a study on the problem of designing non-fragile _H∞$H_{\infty }$ filters with sparse structure for linear discrete-time systems. The filters to be designed with sparse structure are assumed to be with additive gain variations, which are resulted from filter implementations. Firstly, a class of sparse structures is specified from a given fully parameterized _H∞$H_{\infty }$ filter. Then, an LMI-based procedure for designing non-fragile _H∞$H_{\infty }$ filters with the sparse structure is provided. The resulting design guarantees the augmented system asymptotically stable and the _H∞$H_{\infty }$ attenuation level less than a prescribed level. A numerical example is given to illustrate the proposed method.     

H∞ control for network-based systems with time-varying delay and packet disordering

The H_∞ control problem is investigated in this paper for a class of networked control systems (NCS) with time-varying delay and packet disordering. A new model is proposed to describe the packet disordering phenomenon and then converted into a parameter-uncertain system with multi-step delay. Based on the obtained system model, a sufficient condition for robust stability of the NCS is derived. Furthermore, an optimization problem with linear matrix inequalities (LMIs) constraints is formulated to design the state feedback H_∞ controller such that the closed-loop NCS is robust stable and has an optimal H_∞ disturbance attenuation level. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.     

H∞ control of singular time-delay systems via discretized Lyapunov functional

This paper addresses the problem of robust H_∞ control for uncertain continuous time singular systems with state delays. A new singular-type complete quadratic Lyapunov-Krasovskii functional (LKF) is introduced, which combines with the discretization LKF method to synthesis problems. An improved bounded real lemma (BRL) is presented to ensure the system to be regular, impulse free and stable with H_∞ performance condition. Based on the BRL, a memoryless state feedback controller is designed via linear matrix inequalities (LMIs), which greatly reduces the disturbance attenuation level. Numerical examples are given to illustrate improvements over some existing results.     

H2 and H∞ optimal model reduction using genetic algorithms

The mathematical modeling of most physical systems, such as aerospace systems, heat processes, telecommunication systems, transmission lines and chemical reactors, results in complex high order models. The complexity of the models imposes a lot of difficulties in analysis, simulation and control designs. Several analytical model reduction techniques have been proposed in literature over the past few decades to reduce these difficulties. However, most of the optimal techniques follow computationally demanding, time consuming, iterative procedures that usually result in non-robustly stable models with poor frequency response resemblance to the original high order model in some frequency ranges. Genetic Algorithm (GA) has proved to be an excellent optimization tool in the past few years. Therefore, the aim of this paper will be to use GA to solve H₂ and H_∞ norm model reduction problems, and help obtain globally optimized nominal models.     

A switched system approach to H∞ control of networked control systems with time-varying delays

This paper is concerned with the H_∞ control problem for a class of networked control systems (NCSs) with time-varying delay that is less than one sampling period. By applying a new working mode of the actuator and considering state feedback controllers, a new discrete-time switched system model is proposed to describe the NCS. Based on the obtained switched system model, a sufficient condition is derived for the closed-loop NCS to be exponentially stable and ensure a prescribed H_∞ performance level. The obtained condition establishes relations among the delay length, the delay variation frequency, and the system performances of the closed-loop NCS. Moreover, a convex optimization problem is formulated to design the H_∞ controllers which minimize the H_∞ performance level. An illustrative example is given to show the effectiveness of the proposed results.     

Finite-time H∞ control of switched systems with mode-dependent average dwell time

This paper is concerned with finite-time _H∞$H_{\infty }$ control problem for a class of switched linear systems by using a mode-dependent average dwell time (MDADT) method. The switching signal used in this paper is more general than the average dwell time (ADT), in which each mode has its own ADT. By combining the MDADT and Multiple Lyapunov Functions (MLFs) technologies, some sufficient conditions, which can guarantee that the corresponding closed-loop system is finite-time bounded with a prescribed _H∞$H_{\infty }$ performance, are derived for the switched systems. Moreover, a set of mode-dependent dynamic state feedback controllers are designed. Finally, two examples are given to verify the validity of the proposed approaches.     

H∞ filtering for linear neutral systems with mixed time-varying delays and nonlinear perturbations

In this paper, the problem of H_∞ filtering for neutral systems with mixed time-varying delays and nonlinear perturbations is investigated. Some new delay-dependent sufficient conditions are presented to ensure that the filtering error system is asymptotically stable with a prescribed level of H_∞ noise attenuation. In addition, the design procedures for the existence of such filter are presented in terms of a set of linear matrix inequalities (LMIs). Slack variables and convex combination technique are adopted to reduce the conservatism of obtained results. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method.     

A delay-derivative-dependent approach to robust H∞ filter design for uncertain systems with time-varying distributed delays

This paper focuses on the problem of robust H∞ filter design for uncertain systems with time-varying state and distributed delays. System uncertainties are considered as norm-bounded time-varying parametric uncertainties. The delays are assumed to be time-varying delays being differentiable uniformly bounded with delay-derivative bounded by a constant, which may be greater than one. A new delay-derivative-dependent approach of filter design for the systems is proposed. A novel Lyapunov-Krasovskii functional (LKF) is employed, and a tighter upper bound of its derivative is obtained by employing an inequality and using free-weighting matrices technique, then the proposed result has advantages over some existing results, in that it has less conservatism and it enlarges the application scope. An improved sufficient condition for the existence of such a filter is established in terms of linear matrix inequality (LMI). Finally, illustrative examples are given to show the effectiveness and reduced conservatism of the proposed method.     

Nonlinear H∞ robust control applied to F-16 aircraft with mass uncertainty using control surface inverse algorithm

In this paper, an analytic solution of nonlinear H_∞ robust controller is first proposed and used in a complete six degree-of-freedom nonlinear equations of motion of flight vehicle system with mass and moment inertia uncertainties. A special Lyapunov function with mass and moment inertia uncertainties is considered to solve the associated Hamilton-Jacobi partial differential inequality (HJPDI). The HJPDI is solved analytically, resulting in a nonlinear H_∞ robust controller with simple proportional feedback structure. Next, the control surface inverse algorithm (CSIA) is introduced to determine the angles of control surface deflection from the nonlinear H_∞ control command. The ranges of prefilter and loss ratio that guarantee stability and robustness of nonlinear H_∞ flight control system implemented by CSIA are derived. Real aerodynamic data, engine data and actuator system of F-16 aircraft are carried out in numerical simulations to verify the proposed scheme. The results show that the responses still keep good convergence for large initial perturbation and the robust stability with mass and moment inertia uncertainties in the permissible ranges of the prefilter and loss ratio for which this design guarantees stability give same conclusion.