Stochastic Stability Criteria Research Articles

Finite-time output feedback control for a class of stochastic low-order nonlinear systems with output function

This paper studies the problem of finite-time output feedback stabilisation for a class of stochastic low-order nonlinear systems with output function. Under the assumption that output function is continuous, by generalising the adding a power integrator technique, constructing a new implementable reduced-order observer and using the stochastic finite-time stability criterion, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee finite-time stability in probability of the closed-loop system. A simulation example is provided to verify the effectiveness of the proposed design method.

Robust State-Estimator-Based Control of Uncertain Semi-Markovian Jump Systems Subject to Actuator Failures and Time-Varying Delay

This note presents a reformed state-estimator-based adaptive control strategy for uncertain delayed semi-Markovian jump systems (DSMJS) via sliding mode technique. In comparison to most literature results requiring exact prior knowledge of system time-delay, a linear state estimator not linking any control inputs is developed to cope with the case with unknown state delays. By virtue of the acquired state estimation, the establishment of both a new switching surface of linear-type and the involved adaptive controller is provided, and the devised controller could not only admit the assigned SSL's reachability in limited time but also operate on the DSMJS as desired despite the hidden actuator failures and unknowable time-delays. Also, a new sufficient stochastic stability criterion serving as a crucial solution to the control parameters of the resultant plant is inferred. The method also holds in a similar fashion for uncertain plants with no time-delays and/or no switching case. Eventually, the raised method is verified by numerical examples.

A novel memory stabilization controller design for descriptor Markovian jump systems with time-varying delays

This paper is focused on the stochastic stability and controller design of descriptor Markovian jump systems with time-varying delays. For achieving this goal, systems are decomposed into differential-algebraic equations firstly. A modified mode-dependent Lyapunov-Krasovskii functional (LKF) and a memory state feedback controller are constructed on the basis of the state decomposition. Then, combining the auxiliary functions integral inequality and the extended reciprocally convex matrix inequality (ERCMI), an ameliorative stochastic stability criterion is obtained. Based on this novel stability condition, the designed controller is used to make sure the closed-loop systems are stochastically stable. Finally, the effectiveness of presented results is confirmed with some numerical examples.

Stochastic finite-time stability and stabilization for stochastic nonlinear systems with impulse effects

In this paper, some unified stochastic finite-time stability (SFTS) criteria are derived for the impulsive stochastic nonlinear systems by using the stochastic analysis theory, stopping time technology, Lyapunov approach and limit average dwell time (LADT) technology when the impulse effect is destabilizing impulse or stabilizing impulse. Meanwhile, in order to achieve stochastic finite-time stabilization for stochastic nonlinear systems, the impulse control approach is also obtained, which can be divided into two cases: (1) A stochastic finite-time instable (SFTI) stochastic system can become SFTS under the impulse control strategy; (2) A SFTS stochastic system can keep the SFTS under the impulsive disturbance. Furthermore, by using the impulse dependent average dwell time (IDADT) technology, the results are also established for the multiple impulse effects, i.e. destabilizing impulse and stabilizing impulse exist in the system simultaneously. Finally, two useful examples are provided.

Stochastic quantized control for memristive neural networks with mixed semi-Markov jump and sampled-data communications using a novel approach

In this paper, the issue of stability and stabilization for semi-Markov jump memristive neural networks (SMJMNNs) with stochastic quantized sampled-data control (QSDC) law is addressed. Firstly, a memristive neural network (MNN) model with mixed semi-Markov jump is established in the framework of the three independent Markov chains. Then, a stochastic QSDC scheme is proposed, in which semi-Markov jump parameters (SMJPs) in the gain matrices, quantization parameters and system connection weight matrices are different from each other. On the other hand, since signal transmission may be delayed, the influence of transmission delay is considered in the proposed stochastic QSDC scheme. Based on the above, a more general weak infinitesimal operator about the three semi-Markov processes (SMPs) is first given to deal with stochastic Lyapunov functionals (LFs). To reduce the conservatism of the obtained results, stochastic LFs about the two-sided closed-loop functions are constructed in the framework of the sampling patterns ϑ(tk) to ϑ(t) and ϑ(t) to ϑ(tk+1). Then, based on the novel constructed LFs, stochastic stability criterion for SMJMNNs is established by combining with stochastic QSDC law. Finally, the numerical simulation examples are provided to verify the validity and less conservatism of the obtained theoretical results.

Decentralized observer-based control for interconnected fractional-order stochastic systems under input saturation using partial state variables

This paper deals with issues of stochastic stability and decentralized control for interconnected fractional-order stochastic systems (IFSSs) with input saturation. At first, model of the IFSS is built. Meanwhile, a decentralized control technique in view of observer and partial state variables of the system is proposed. This method can simultaneously realize the observation and control for the system only by observing and controlling partial state variables. And both observation cost and control cost can also be decreased. Then, by means of fractional calculus theory, a novel stability analysis is shown, and relational stochastic stability criteria are derived. Related results can be applied not only to the common IFSSs, but also to many actual systems, for example power systems and chaotic systems. Additionally, range of the order for the IFSSs is also further enlarged. Eventually, validity of the results is verified via several numerical simulations, and advantages for the control technique developed are presented by comparison.

Fixed-Time Fuzzy Adaptive Control of Manipulator Systems Under Multiple Constraints: A Modified Dynamic Surface Control Approach

In this article, the fixed-time fuzzy adaptive tracking control problem is studied for a class of one-link manipulator systems with stochastic disturbances and multiple constraints. First, a modified dynamic surface control technique is proposed for the stochastic system, which provides a useful filtering solution to the fixed-time control of the stochastic nonlinear systems. Then, an extended stochastic fixed-time stability criterion is introduced to simplify the complex discussion process of stability analysis instead of existing fixed-time stability criteria. By using the unified barrier function, the constrained nonlinear system can be transformed into the nonconstrained nonlinear system. Moreover, a fuzzy adaptive controller is constructed with the funnel error transformation function, which improves the transient response of the system. The control objective of this article is that the steady-state error can be driven to the prespecified funnel in a fixed time based on the Lyapunov stability theorem and the extended stochastic fixed-time stability criterion. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

A new design method to global asymptotic stabilization of strict-feedforward stochastic nonlinear time delay systems

The stabilization problems of stochastic nonlinear systems remain challenging because many new obstacles will be encountered and need to be cautiously handled. This paper discusses the global asymptotic stabilization problem of stochastic nonlinear systems which possess strict-feedforward structure and multiple time delays. In the first place, we are trying to transform the considered system into an equivalent one by constructing the novel parameter-dependent state feedback controller and the suitable coordinate transformation. And then, through using the stochastic time delay system stability criterion and introducing the proper Lyapunov–Krasovskii functional, the global asymptotic stability of stochastic closed-loop system is proved. Finally, simulation results show the effectiveness of the parameter-dependent state feedback controller.

Adaptive sliding mode control of Markov jump systems with completely unknown mode information

AbstractThis paper aims to investigate the problem of adaptive sliding mode control for Markov jump systems with deficient transition probability. Different from the existing literature, we propose a novel method to design a mode‐dependent sliding mode controller when the mode information is completely unknown, while the controller gain parameters can be designed by solving feasible conditions. Firstly, by designing an integral‐type sliding surface, on which an ideal sliding mode dynamics is obtained. Then, for different types of mode transition information, a set of feasible easy‐checking stochastic stability criteria are proposed for the sliding mode dynamics in terms of strict linear matrix inequalities. Further, relying on the parameters obtained from the stability criteria, an adaptive sliding mode controller is successfully designed with respect to different types of system mode transition information. Finally, a numerical example is provided to illustrate the advantage of the developed strategy.

Predictive output feedback control of networked control system with Markov DoS attack and time delay

SummaryThis paper studies the networked control systems (NCS) predictive output feedback control issue with random time delay and denial of service (DoS) attacks. The mathematical description of the random DoS attacks and time delays in controller‐to‐actuator (C‐A) and sensor‐to‐controller (S‐C) communication channels is researched based on Markov stochastic theory. Considering the random characteristics of network‐induced attacks and delays, the closed‐loop NCS is modeled as a discrete‐time linear system with Markov DoS attack and time delay. The stochastic stability criterion of a class of networked predictive control systems with random attack and delay is proposed based on Lyapunov stability theory and the predictive compensation control method. The networked model predictive output feedback controller is designed by applying the parameter compensation method and linear matrix inequality (LMI) technique. Numerical simulation results are proposed to verify the effectiveness of the proposed control strategy.

Dynamic event-triggered [formula omitted] control for markov jump systems with input saturation

This paper is mainly to explore H∞ state feedback control problem for Markov jump systems (MJSs) with input saturation. To avoid the waste of network resources, a dynamic event-triggered mechanism (DETM) is proposed from system plant to controller, which produces a larger interval between two consecutive events compared with the traditional static one. On the basis of this model, sufficient criteria for stochastic stability of the controlled MJSs are derived by linear matrix inequalities (LMIs) and the controllers are designed. Then the maximum estimate of the domain of attraction (DOA) is obtained by the optimization procedure. Finally, examples show that the proposed DETM has better properties of saving resources than static event-triggered mechanism (ETM) while maintaining the same performance.

Fuzzy SMC for Quantized Nonlinear Stochastic Switching Systems With Semi-Markovian Process and Application.

This article is concerned with the issue of quantized sliding-mode control (SMC) design methodology for nonlinear stochastic switching systems subject to semi-Markovian switching parameters, T-S fuzzy strategy, uncertainty, signal quantization, and nonlinearity. Compared with the previous literature, the quantized control input is first considered in studying T-S fuzzy stochastic switching systems with a semi-Markovian process. A mode-independent sliding surface is adopted to avoid the potential repetitive jumping effects. Then, by means of the Lyapunov function, stochastic stability criteria are proposed to be dependent of sojourn time for the corresponding sliding-mode dynamics. Furthermore, the fuzzy-model-based SMC law is proposed to ensure the finite-time reachability of the sliding-mode dynamics. Finally, an application example of a modified series dc motor model is provided to demonstrate the effectiveness of the theoretical findings.

Stochastic stability and stabilization of positive Markov jump linear impulsive systems with time delay

This paper investigates the stochastic stability and stabilization of positive Markov jump linear impulsive systems (PMJLIS) with time delay. First, by choosing appropriate co-positive Lyapunov–Krasovskii functional and using the impulsive average dwell-time method, a stochastic stability criterion is provided for PMJLIS with time delay. Based on this criterion, for PMJLIS with time delay, the stabilization conditions are given using state feedback and impulse feedback, respectively. According to this criteria, the stochastic stability of the systems can be judged and the controllers can be designed only from some relations of the coefficient matrices, Markov jump parameters and delay. To illustrate the main results, a simulation example is provided at the end with a state-feedback controller and an impulsive controller is designed, respectively, which makes the corresponding closed-loop systems be positive, globally asymptotically stable in probability and globally asymptotically stable in mean.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay.

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Stochastic Finite-Time Stability for Stochastic Nonlinear Systems with Stochastic Impulses

In this paper, some novel stochastic finite-time stability criteria for stochastic nonlinear systems with stochastic impulse effects are established. The results in this paper blackgeneralized the related results in from two aspects: 1. the model in is the deterministic systems, which means that the noise effect that can be described as a symmetric Markov process Brownian motion is considered in our models; 2. the stochastic finite-time stability criterion is established in this paper, not the asymptotic stability and the input-to-state stability that are studied in the form literature. Finally, an example is given to show the significance blackand usefulness of our results.

Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks

This paper investigates, through designing an event-triggered sampled-data mechanism, the stochastic stabilization of Markovian jump quaternion-valued neural networks (QVNNs) with partially unknown transition probabilities. First, since the multiplication of quaternions is not commutative, the Markovian jump QVNNs are decomposed into four real-valued neural networks. Then, by constructing a novel augmented Lyapunov–Krasovskii functional (LKF), it is containing more hybrid features, in which concerning the practical sampling pattern, and using the convex combinatorial optimization and inequality technique, the stabilization condition is proposed in the form of linear matrix inequalities (LMIs). Furthermore, the desired event-triggered sampled-data controller gains are obtained for the closed-loop Markovian jump QVNNs with partially unknown transition probability. Finally, the viability and validness of the obtained results are confirmed via three numerical examples.

Stochastic stabilization of Markovian jump neutral systems with fractional Brownian motion and quantized controller

This paper explores the delay dependent stochastic stabilization of Markovian jump neutral systems (MJNS) which are modeled by fractional Brownian motion(fBm) via a quantized controller. A function Round quantizer is introduced which solves the model uncertainties and the nonlinear part by a uniform operator. Then by structuring a Lyapunov–Krasovskii functional (LKF) and the aid of linear matrix inequalities (LMIs) method, a stochastic stability criterion is achieved. Last, different parameters are selected to simulate the effectiveness of our findings.

Finite-Time Event-Triggered Control for Semi-Markovian Switching Cyber-Physical Systems With FDI Attacks and Applications

This paper addresses the finite-time event-triggered control problem for nonlinear semi-Markovian switching cyber-physical systems (S-MSCPSs) under false data injection (FDI) attacks. Compared with the traditional time-triggered mechanism, the proposed event-triggered scheme (ETS) can effectively avoid network resource waste. Considering the network-induced delay in the modeling, a closed-loop system model with time delay is established in the unified framework. By the use of a mode-dependent piecewise Lyapunov-Krasovskii functional (LKF), stochastic finite-time stability (SFTS) criteria are established for the resultant closed-loop system. Then, some solvability conditions are established for the desired finite-time controller in light of a linear matrix inequality framework. Finally, an application example of vertical take-off and landing helicopter model (VTOLHM) is provided to demonstrate the effectiveness of the theoretical findings.

Event-generator-based H∞ control of fuzzy distributed parameter systems

This paper studies the adaptive event-based H∞ control problem for a class of T-S fuzzy distributed parameter system with parameter uncertain and actuator faults. To overcome the drawback of the period control scheme, an event-triggered control scheme with adaptive threshold is proposed to minimize the number of unnecessary sampled data transmission and to reduce the update frequency of the controller. Furthermore, a T-S fuzzy controller based on the adaptive event-triggered sampled data is designed to ensure the stochastic exponential stability of the distributed parameter system with H∞ disturbance attenuation performance. Based on a new Lyapunov functional and inequality technique, the stochastic exponential stability criterion of the closed-loop system is obtained, and the controller parameters are designed. The new developed inequality can reduce the conservatism of the stability criterion. Finally, the effectiveness of the theoretical calculation results is verified by numerical simulation, and the results are compared with the relevant literature in the simulation, showing that the methods and results in this paper are less conservative.

Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control

This paper investigates the stochastic stabilization of Markov jump quaternion-valued neural networks (QVNNs) using a sampled-data control strategy. Firstly, Markov jump QVNNs are decomposed into two complex-valued systems using the plural decomposition method because the multiplication of quaternions is not commutative. Secondly, the existence and uniqueness of the equilibrium point of the Markov jump QVNNs is proved according to the theory of homeomorphism mapping. Thirdly, by choosing a suitable Lyapunov-Krasovskii functional and combining some inequality techniques, a new stochastic stability criterion is established for the Markov jump QVNNs. Based on this, several verifiable sufficient conditions for the stochastic stabilization of Markov jump QVNNs with sampled-data control are ensured. Finally, the correctness and effectiveness of the proposed method are verified by two numerical examples.