Asynchronous Learning-Based Output Feedback Sliding Mode Control for Semi-Markov Jump Systems: A Descriptor Approach

This paper presents an asynchronous output-feed-back control strategy of semi-Markovian systems via sliding mode-based learning technique.Compared with most literature results that require exact prior knowledge of system state and mode information,an asynchronous output-feedback sliding sur-face is adopted in the case of incompletely available state and non-synchronization phenomenon.The holonomic dynamics of the sliding mode are characterized by a descriptor system in which the switching surface is regarded as the fast subsystem and the system dynamics are viewed as the slow subsystem.Based upon the co-occurrence of two subsystems,the sufficient stochastic admissibility criterion of the holonomic dynamics is derived by utilizing the characteristics of cumulative distribution functions.Furthermore,a recursive learning controller is formulated to guarantee the reachability of the sliding manifold and realize the chattering reduction of the asynchronous switching and sliding motion.Finally,the proposed theoretical method is substantia-ted through two numerical simulations with the practical contin-uous stirred tank reactor and F-404 aircraft engine model,respectively.

Output feedback control for semi-Markovian jump systems with time-varying delay

This study investigates the problem of output feedback control for semi-Markovian jump systems(S-MJLSs)with time-varying delay.Due to the relaxed conditions on the stochastic process,the S-MJLSs are with time-varying transition rates and can describe a broader class of dynamical systems than the traditional Markovian jump linear systems.Specially,first,by using a novel free-matrix-based integral inequality(FMBII)including well-known integral inequalities as special cases,the H∞performance analysis and mode-dependent nonrational synthesis conditions for the underlying S-MJLSs are developed,respectively.Secondly,the conditions obtained in this paper are formulated in terms of linear matrix inequalities(LMIs),which can be efficiently solved via standard numerical software.Finally,numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.

Security control of positive semi-Markovian jump systems with actuator faults

Actuator faults usually cause security problem in practice.This paper is concerned with the security control of positive semi-Markovian jump systems with actuator faults.The considered systems are with mode transition-dependent sojourn-time distributions,which may also lead to actuator faults.First,the time-varying and bounded transition rate that satisfies the mode transition-dependent sojourn-time distribution is considered.Then,a stochastic co-positive Lyapunov function is constructed.Using matrix decomposition technique,a set of state-feedback controllers for positive semi-Markovian jump systems with actuator faults are designed in terms of linear programming.Under the designed controllers,stochastic stabilization of the systems with actuator faults are achieved and the security of the systems can be guaranteed.Furthermore,the proposed results are extended to positive semi-Markovian jump systems with interval and polytopic uncertainties.By virtue of a segmentation technique of the transition rates,a less conservative security control design is also proposed.Finally,numerical examples are provided to demonstrate the validity of the presented results.

Event-Triggered Control of Positive Semi-Markovian Jump Systems Without/with Input Saturation

This paper is concerned with the event-triggered control of positive semi-Markovian jump systems without/with input saturation.The considered systems are subject to a stochastic semi-Markovian process whose sojourn time is dependent on a non-exponential distribution.First,an event-triggering condition is introduced in a linear form for the systems.A class of event-triggered feedback controllers is proposed using matrix decomposition technique.By using a stochastic co-positive Lyapunov function,the systems’positivity and stability are guaranteed.Then,the obtained results are developed for the systems with input saturation.A cone set is chosen as the attraction domain and the corresponding attraction domain gain matrix is designed in terms of standard linear programming approach.Finally,two numerical examples are provided to verify the validity and effectiveness of the presented theoretical findings.

A Double Sensitive Fault Detection Filter for Positive Markovian Jump Systems With A Hybrid Event-Triggered Mechanism

This paper is concerned with the double sensitive fault detection filter for positive Markovian jump systems. A new hybrid adaptive event-triggered mechanism is proposed by introducing a non-monotonic adaptive law. A linear adaptive event-triggered threshold is established by virtue of 1-norm inequality.Under such a triggering strategy, the original system can be transformed into an interval uncertain system. By using a stochastic copositive Lyapunov function, an asynchronous fault detection filter is designed for positive Markovian jump systems(PMJSs) in terms of linear programming. The presented filter satisfies both L_-gain(?_-gain) fault sensitivity and L_1(?_1)internal differential privacy sensitivity. The proposed approach is also extended to the discrete-time case. Finally, two examples are provided to illustrate the effectiveness of the proposed design.

Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities

This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems(MJTDSs),whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance,auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function(ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally,numerical examples are given to show the effectiveness and the merits of the proposed method.

Exponential passive filtering for a class of nonlinear jump systems

The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.

Robust H-infinity filter design for uncertaintime-delay singular stochastic systems withMarkovian 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 It6 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.

Delay-dependent Stability Analysis for Markovian Jump Systems with Interval Time-varying-delays

This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities （LMIs）, less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.

Robust reliable H-infinity control for nonlinear uncertain stochastic time-delay systems with Markovian jumping parameters

This paper deals with the problems of robust reliable exponential stabilization and robust stochastic stabilization with H-infinity performance for a class of nonlinear uncertain time-delay stochastic systems with Markovian jumping parameters. The time delays are assumed to be dependent on the system modes. Delay-dependent conditions for the solvability of these problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that the desired state feedback controller can be designed by solving a set of linear matrix inequalities. Finally, the simulation is provided to demonstrate the effectiveness of the proposed methods.

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.

Exponential stability for uncertain neutral systems with Markov jumps

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities （LMIs）, which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.

Sliding Mode Control for Nonlinear Markovian Jump Systems Under Denial-of-Service Attacks

This paper investigates the sliding mode control(SMC) problem for a class of discrete-time nonlinear networked Markovian jump systems(MJSs) in the presence of probabilistic denial-of-service(Do S) attacks. The communication network via which the data is propagated is unsafe and the malicious adversary can attack the system during state feedback. By considering random Denial-of-Service attacks, a new sliding mode variable is designed, which takes into account the distribution information of the probabilistic attacks. Then, by resorting to Lyapunov theory and stochastic analysis methods, sufficient conditions are established for the existence of the desired sliding mode controller, guaranteeing both reachability of the designed sliding surface and stability of the resulting sliding motion.Finally, a simulation example is given to demonstrate the effectiveness of the proposed sliding mode control algorithm.

Guaranteed control performance robust LQG regulator for discrete-time Markovian jump systems with uncertain noise

Robust LQG problems of discrete-time Markovian jump systems with uncertain noises are investigated. The problem addressed is the construction of perturbation upper bounds on the uncertain noise covariances so as to guarantee that the deviation of the control performance remains within the precision prescribed in actual problems. Furthermore, this regulator is capable of minimizing the worst performance in an uncertain case. A numerical example is exploited to show the validity of the method.

Delay-dependent stabilization of singular Markovian jump systems with state delay

This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays. A delay-dependent condition is established for the considered system to be regular, impulse free and stochastically stable. Based on the condition, a design algorithm of the desired state feedback controller which guarantees the resultant closed-loop system to be regular, impulse free and stochastically stable is proposed in terms of a set of strict linear matrix inequalities （LMIs）. Numerical examples show the effectiveness of the proposed methods.

On necessity proof of strict bounded real lemma for generalized linear systems with finite discrete jumps

Some preliminary results on strict bounded real lemma for time-varying continuous linear systems are proposed, where uncertainty in initial conditions, terminal cost and extreme of the cost function are dealt with explicitly. Based on these results, a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.

State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems(MJLSs) with controllable mode transition probability matrix(MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.

On Optimal Fault Detection for Discrete-time Markovian Jump Linear Systems

这份报纸为分离时间的 Markovian 处理差错察觉的问题跳线性系统(MJLS ) 。把一个基于观察员的差错察觉过滤器(FDF ) 用作一个剩余发电机， FDF 的设计为最大化随机的 H/H 或 H/H 表演索引作为一个优化问题被提出。在一个操作符优化方法的帮助下，一个统一最佳的解决方案能被解决 a coupled Riccati 方程导出，这被显示出。数字例子被给显示出建议方法的有效性。

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.