<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for nonlinear stochastic Markov systems with time-delay and multiplicative noise

This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input- and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities (HJIs), the exponential mean square H_∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly, by using fuzzy T-S model approach, the H_∞ controller can be designed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

Fuzzy Static Output Feedback <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control for Nonlinear Systems Subject to Parameter Uncertainties

This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities (LMIs). LMI-based stability conditions for interval type-2 fuzzy static output feedback H_∞ control synthesis are also developed. Several simulation examples are given to show the superiority of the proposed approach.     

H 2/H ∞ control problems of backward stochastic systems

This paper is concerned with the mixed H2/H∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations（BSDEs）.The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H2/H∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H2/H∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state.     

Discrete-time mean-field stochastic <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

The finite horizon H ₂/H _∞ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, the authors derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the solvability of discrete-time mean-field stochastic linearquadratic (LQ) optimal control is presented. Thirdly, based on SBRL and LQ results, this paper establishes a sufficient condition for the existence of discrete-time stochastic H ₂/H _∞ control of meanfield type via the solvability of coupled matrix-valued equations.     

On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise

<正> This paper presents the notions of exact observability and exact detectability for Markovjump linear stochastic systems of Ito type with multiplicative noise (for short,MJLSS).StochasticPopov-Belevith-Hautus (PBH) Criterions for exact observability and exact detectability are respectivelyobtained.As an application,stochastic H_2/H_∞ control for such MJLSS is discussed under exactdetectability.     

Guidance laws based on <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> observer considering measurement noises

Since in practice the line-of-sight (LOS) rate is difficult for a pursuer to measure accurately, the robust nonlinear H _∞ observer is applied to estimate it using LOS azimuths without any priori information of target maneuvers or its estimate in the presence of measurement noise. A threedimensional guidance law is implemented by replacing the LOS rate with their estimates using only relative range, speed, and LOS azimuths. The stability analyses and performed simulations results show that the presented approach is effective.     

On Robust Stability of a Class of Uncertain Nonlinear Systems with Time—Varying Delay

The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions on robust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay. Some previous results are improved and a numerical example is given to demonstrate the validity of our results.     

<Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript> disturbance attenuation for a class of time-delay Hamiltonian systems

This paper considers the problem of L ₂-disturbance attenuation for a class of time-delay port-controlled Hamiltonian systems. A γ-dissipative inequality is established by using a proper control law and a storage function. Then based on the Razumikhin stability theorem, a sufficient condition is proposed for the asymptotically stability of the closed-loop system. Finally, the authors investigate the case that there are time-invariant uncertainties belonging to some convex bounded polytypic domain and an L ₂ disturbance attenuation control law is proposed. Study of illustrative example with simulation shows that the presented method in this paper works very well in the disturbance attenuation of time-delay Hamiltonian systems.     

Design of unknown input observer with H∞ performance for linear time-delay systems

A unknown input observer (UIO) design for a class of linear time-delay systems when the observer error can't completely decouple from unknown input is dealt with. A sufficient condition to its existence is presented based on Lyapunov stability method Design problem of the proposed observer is formulated in term of linear matrix inequalities. Two design problems of the observer with internal delay and without internal delay are formulated Based on H_∞ control theory in time-delay systems, the proposed observer is designed in term of linear matrix inequalities (LMI). A design algorithm is proposed The effective of the proposed approach is illustrated by a numerical example     

Sampled-Data H∞ Dynamic Output Feedback Controller Design for Fuzzy Markovian Jump Systems

This paper considers the issue of H_∞ dynamic output feedback controller design for T-S fuzzy Markovian jump systems under time-varying sampling with known upper bound on the sampling intervals. The main aim is to realize sampled-data fuzzy dynamic output feedback control so as to demonstrate the stochastic stability and H_∞ performance index of the closed-loop sampled-data fuzzy Markovian jump systems. Then, by making the most of the information within the sampling interval,...     

Delay-dependent decentralized H∞ filtering for uncertain interconnected systems

This article considers delay dependent decentralized H∞ filtering for a class of uncertain interconnected systems, where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions. First, combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices, a sufficient condition of the existence of the robust decentralized H∞ filter is derived, which makes the error systems asymptotically stable and satisfies the H∞ norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties. Then, the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation. Finally, the numerical simulation shows the efficiency of the main results.     

Properties of storage functions and applications to nonlinear stochastic <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

This paper discusses the properties of the storage functions for a class of nonlinear stochastic systems. Some necessary and sufficient conditions for a function to be a storage function are derived. As applications, the finite and infinite horizon nonlinear stochastic H _∞ controls for systems with state, control, and external disturbance dependent noise are investigated, which generalize the previous results.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for stochastic systems with Poisson jumps

This paper discusses the H _∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H _∞ control design is also extended to such systems.     

非线性时滞系统自适应输出反馈跟踪控制

针对一类参数化非线性时滞输出反馈系统,提出了一种自适应输出跟踪控制器的设计方案。引入时滞滤波器估计未知系统状态,采用backstepping技术设计控制律和参数自适应律,运用占优方法处理非线性时滞项,从而放宽了对非线性时滞函数的要求,实现了对给定目标轨线的全局渐近跟踪,同时保证闭环系统所有信号一致有界。基于Lyapunov-Krasoviskii泛函方法证明了整个闭环系统的稳定性。实例仿真说明了该方案的可行性。     

Robust reliable H∞ control for discrete-time Markov jump linear systems with actuator failures

The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.     

Fault Detection for Complex Systems with Channel Fadings,Randomly Occurring Multiple Delays and Infinitely Distributed Delays

This paper is concerned with the fault detection(FD) problem for a class of discretetime stochastic systems with channel fadings, randomly occurring multiple communication delays,and infinitely distributed delays. All of the three phenomena have the characteristics of randomly occurring and three sequences of stochastic variables which are mutually independent but obey the Bernoulli distribution are employed to describe them. The aim of this paper is to design an FD filter such that the FD dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Intensive analysis is utilized to derive the sufficient conditions for the designed FD filter, which guarantees the exponential stability and the prescribed H∞ performance. FD filter parameters are obtained by solving a convex optimization problem. An illustrative example is provided to demonstrate the effectiveness of the FD design scheme.     

ROBUST H∞ CONTROL FOR UNCERTAIN NONLINEAR SYSTEMS

This paper studies the robust H∞ disturbance attenuation with internal stability for uncertain nonlinear control systems. By adding one power integrator technique, this paper designs a explicit smooth robust dynamic feedback law while rejecting the disturbance to any specified degree of accuracy. Further, the example and simulation results show the effectiveness of the proposed schemes.     

时间滞后系统鲁棒控制方法及在飞控中的应用

给出了一种时间滞后系统的鲁棒控制方法。通过对系统鲁棒稳定性条件不等式的等价变形，得到了该不等式可解的条件并且大大简化了不等式；从而得到了包含复极点的时间滞后系统的鲁棒稳定性判据。针对系统具有多个时间滞后问题，运用系统单个滞后的鲁棒稳定性不等式判据，给出了包含复极点的简明鲁棒稳定性判别式。该方法接近于普通的状态反馈设计，便于工程实现。飞行器控制设计的仿真计算结果表明，采用新方法可以得到满意的设计结果。     

Study on Variation of Parameters Formula and Stability for Impulsive Time－Delay Nonlinear Large Scale Systems

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