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.

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 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.

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.

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.

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.

Nonlinear H_∞ filtering for interconnected Markovian jump systems

The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentially meansquare stable and ensures a prescribed H∞ performance. A sufficient condition for the solvability of this problem is given in terms of linear matrix inequalities（LMIs）. A simulation example is presented to demonstrate the effectiveness of the proposed design approach.

On passivity of state delayed stochastic jump systems

Based on the definition of passivity extended from deterministic system, the sufficient condition on passivity of stochastic jump system is given against unknown state time delay. By means of memoryless state feedback, a class of state delayed stochastic jump systems may be led to passive. The feedback controllers are mode-dependent and can be constructed in terms of the solutions of a set of coupled linear matrix inequalities. A numerical example illustrates the results.

Variable structure control for descriptor Markovian jump systems subject to partially unknown transition probabilities

The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) technique,a sufficient condition is presented, under which the DMJSs subject to PUTPs are stochastically admissible. Secondly,a novel sliding surface function based on the system state and input is constructed for DMJSs subject to PUTPs; and a dynamic sliding mode controller is synthesized, which guarantees that state trajectories will reach the pre-specified sliding surface in finite time despite uncertainties and disturbances. The results indicate that by checking the feasibility of a series of LMIs,the stochastic admissibility of the overall closed loop system is determined. Finally,the validity of the theoretical results is illustrated with the example of the direct-current motor. Furthermore,compared with the existing literature,the state convergence rate,buffeting reduction and overshoot reduction are obviously optimized.

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.

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

The design of robust H-infinity controller for uncertain discrete-time Markovianjump systems with actuator saturation is addressed in this paper. The parameter uncertainties are assumed to be norm-bounded. Linear matrix inequality （LMI） conditions are proposed to design a set of controllers in order to satisfy the closed-loop local stability and closed-loop H-infinity performance. Using an LMI approach, a set of state feedback gains is constructed such that the set of admissible initial conditions is enlarged and formulated through solving an optimization problem. A numerical example is given to illustrate the effectiveness of the proposed methods.

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,a suitable closed-loop function is constructed and the integral terms are handled by using free weighted matrix method and improved integral inequality technique.Numerical example and single-link robot arm are presented to show the effectiveness of the developed method.

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.

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.

Robust mode-dependent control for discrete-time singular Markovian jump systems with time-varying delay

This study investigates the problem of robust mode-dependent control for a class of discrete-time singular Markovian jump systems with time-varying delay.Using the Lyapunov functional method and delay decomposition approach,Linear matrix inequality(LMI)-based sufficient conditions for the stochastic stability and robust modedependent control are developed,which guarantee the considered systems to be regular,causal and stochastically stabilisable.Finally,numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.

Asynchronous Output Regulation Control for Continuous-Time Markovian Jump Systems with Colored-Noise

The output regulation control problem for the Markovian jump systems with colored-noise is proposed in this paper.Since the modes mismatch problem often exists in the Markovian switching system,the authors design a modes asynchronous controller with an internal model form,which can not only deal with external disturbance,but also reduce the influence of stochastic noise on the system,such that the mean square of the regulation error can be made arbitrarily small by turning the designed parameters.Meanwhile,a criterion of the m-th moment noise-to-state exponential stability is presented for continuous-time Markovian jump systems under the asynchronous control.

Composite Anti-Disturbance Control of Hidden Semi-Markov Jump Systems via Disturbance Observer

This paper focuses on the disturbance suppression issue of hidden semi-Markov jump systems leveraging composite control.The system consists of a semi-Markov layer and an observed mode sequence layer,and it is subject to a matched disturbance generated by an exogenous system and a mismatched disturbance that is norm bounded.The proposal is to design a composite controller based on a disturbance observer to counteract and attenuate the disturbances effectively.By constructing a special Lyapunov function comparison point,the exponential stability is analyzed with the stability criterion in the form of linear matrix inequality is established.Two simulation examples are provided to demonstrate the practical merits of the composite controller relative to the single H_(∞)control.

Positive Observer Design for Positive Markovian Jump Systems with Partly Known Transition Rates

The paper is concerned with positive observer design for positive Markovian jump systems with partly known transition rates. By applying a linear co-positive type Lyapunov-Krasovskii function,a sufficient condition is proposed to ensure the stochastic stability of the error positive system and the existence of the positive observer, which is computed in linear programming. Finally, an example is given to demonstrate the validity of the main results.

Asynchronous Dissipative Control and Robust Exponential Mean Square Stabilization for Uncertain Fuzzy Neutral Markov Jump Systems

This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules.The asynchronous phenomenon is considered between the uncertain fuzzy neutral Markov jump systems modes and asynchronous fuzzy P-D feedback controller modes,which is described by a hidden Markov model.Via using linear matrix inequalities,the desired asynchronous fuzzy P-D feedback controller is obtained,which can ensure that the closed-loop uncertain fuzzy neutral Markov jump systems satisfies robustly exponential mean square stabilization with strict dissipativity.A numerical example and a single-link robot arm are utilized to demonstrate the effectiveness of the method.