semi-Markov Switching Systems Research Articles

Fuzzy Integral Sliding-Mode Control for Nonlinear Semi-Markovian Switching Systems With Application

The issue of sliding-mode control (SMC) design is studied for a class of nonlinear semi-Markovian switching systems (S-MSSs) via T–S fuzzy approach. Compared with previous literature, novel integral sliding-mode surfaces (ISMSs) are developed to depend on the designed controller gains and projection matrices. The aim of this work is to design an appropriate fuzzy SMC law under complex stochastic semi-Markovian switching process. For this purpose, the novel ISMSs are developed under the T–S fuzzy modeling framework. Then, based on the weak infinitesimal operator theory, sufficient conditions are given for stochastic stability criteria relying on the sojourn-time. Furthermore, an appropriate fuzzy SMC law is proposed to drive the state signals onto the predefined fuzzy manifold. Finally, an electric circuit model illustrates the effectiveness of the theoretical findings.

Quantized Fuzzy Finite-Time Control for Nonlinear Semi-Markov Switching Systems

This brief considers quantized control for finite-time synthesis of nonlinear semi-Markov switching systems (S-MSSs) via T-S fuzzy strategy. The stochastic phenomena of structural and parametric changes are modeled by the semi-Markov process, in which the sojourn-time (ST) is deemed to obey a non-exponential distribution. Compared with previous works, the input quantization is firstly investigated for studying the finite-time control via a logarithmic quantizer. A key issue under the consideration is how to design a fuzzy-model-based finite-time control law in the presence of quantized error. For this purpose, by using the key point of Lyapunov function, the finite-time boundedness (FTBs) performance is analyzed via establishing sojourn-time-dependent sufficient conditions within a given finite-time level. Then, the existence of a quantized controller is given in standard LMIs. Finally, an example for an electric circuit shows the effectiveness of the finite-time control scheme.

Finite-Time Observer-Based Sliding Mode Control for Quantized Semi-Markov Switching Systems With Application

This article investigates the problem of sliding mode control (SMC) for semi-Markov switching systems (S-MSSs) with quantized measurement in finite-time level. The transition between different subsystems obeys a stochastic semi-Markov process related to nonexponential distribution. Additionally, due to the sensor information constraints, the state vectors are not always measurable in practice. Moreover, compared with existing results in literature, the output quantization is first considered for finite-time SMC problem via a logarithmic quantizer. Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance onto the overall performance of the system under consideration. First, by the key points of stochastic semi-Markov Lyapunov function and observer design theory, a desired SMC law is constructed to guarantee that the system trajectories can arrive at the specified sliding surface (SSS) within an assigned finite-time level. Then, ST-dependent sufficient conditions are established to ensure the required finite-time boundedness performance including both reaching phase and sliding motion phase. Finally, the applicability of the proposed results is demonstrated by a single-link robot arm model.

Sliding Mode Control for Nonlinear Stochastic Semi-Markov Switching Systems With Application to SRMM

In this paper, the sliding mode control (SMC) design for nonlinear stochastic semi-Markov switching systems (S-MSSs) is studied via the bound of time-varying transition rate matrix, in which semi-Markov switching parameters, stochastic disturbance, uncertainty, and nonlinearity are all considered in a unified framework. The system under consideration is more general, which covers the Markov switching system with sojourn-time-independent transition rate matrix as a special case. Many practical systems subject to unpredictable structural variations can be characterized by nonlinear stochastic S-MSSs with sojourn-time-dependent transition rate matrix. The specific information about the bound of time-varying transition rate matrix is known for the sliding mode controller design. First, by using the stochastic semi-Markov Lyapunov function, sojourn-time-dependent sufficient conditions are developed to guarantee the closed-loop sliding mode dynamics stochastically stable. Then, the SMC law is constructed to ensure the reachability of the sliding mode dynamics in a finite-time level. Finally, one joint of space robot manipulator model is described as nonlinear stochastic S-MSSs to illustrate the validity of the proposed SMC design method.

Finite-time stabilization of T–S fuzzy semi-Markov switching systems: A coupling memory sampled-data control approach

The present draft investigates the finite-time stabilization of T–S fuzzy semi-Markov switching systems by using a coupling memory sampled-data control approach. The main study concerned is how to effectively design the sampled-data control such that closed-loop T–S fuzzy semi-Markov switching systems is finite-time boundedness. By utilizing a Bernoulli distributed sequence, a more general coupling memory fuzzy sampled-data control strategy that involving time delay effect is derived. By virtue of fuzzy-basis-dependent membership functions, an asynchronous approach is proposed for T–S fuzzy semi-Markov switching system. Moreover, the inverted pendulum model is presented to demonstrate the feasibility and validity of the proposed strategies.

Anti-Windup Design for Saturated Semi-Markovian Switching Systems With Stochastic Disturbance

In this brief, we consider the anti-windup design for stochastic semi-Markovian switching systems (S-MSSs) with saturation nonlinearity and stochastic disturbance. In the system under consideration, stochastic S-MSSs with the semi-Markovian process can describe more complex systems in a practical control process. The main motivation of this brief is that the practical system described by stochastic S-MSSs always needs to consider the actuator saturation. To deal with this kind of complex problem, sufficient conditions for stochastic stability (SSY) analysis is developed by the Lyapunov function method. Then, the anti-windup strategy is constructed to make the dynamical system achieves SSY and maximize the domain of attraction. Finally, the simulation results of the practical system show the validity of the proposed method.

Robust finite-time stabilization for positive delayed semi-Markovian switching systems

Robust finite-time stabilization is discussed for positive semi-Markovian switching systems (S-MSSs), in which semi-Markovian process, time-varying delay, external disturbance, and transient performance in finite-time level are all considered in a unified framework. In the system under consideration, finite-time problem can describe transient performance of practical control process. Firstly, some finite-time boundedness and L1 finite-time boundedness criteria for positive delayed S-MSSs are proposed by constructing the stochastic semi-Markovian Lyapunov–Krasovskii functional with mode-dependent integral term. Then, a developed L1 finite-time feedback controller design method is presented to reduce some constraints of input matrices, which guarantees the resulting closed-loop system achieves positivity, finite-time boundedness, and has a prescribed L1 noise attenuation performance index in a novel standard linear programming. Finally, a practical example is illustrated to validate the proposed results by applying a virus mutation treatment model.

Formula omitted] finite-time stabilization for positive semi-Markovian switching systems

This paper investigates robust finite-time stabilization scheme for positive semi-Markovian switching systems (S-MSSs). Semi-Markovian process (SMP), external disturbances, and transient performances at a finite-time level may appear in a controlled system. A more general system model for S-MSSs that covers Markovian switching systems (MSSs) as a special case is suitable for describing some complex systems that are subject to random abrupt changes in structure and parameter. The main motivation for this is that finite-time problems can be used to describe the transient performance of practical industrial control processes. First, under the framework of stochastic semi-Markovian Lyapunov functions theory, some sufficient conditions for finite-time boundedness (FTBs) and L1 FTBs criteria for positive S-MSSs are proposed for all admissible disturbances. Then, a novel L1 finite-time controller design method that employs the gain matrix decomposition method is presented to reduce some conservativeness, thereby guaranteeing that the resulting closed-loop system (RLCS) could achieve positivity, FTBs, and attain a prescribed L1 noise attenuation performance index in standard linear programming (LP). Finally, a practical example is introduced to show the effectiveness of the main theory

Exponential consensus of non‐linear multi‐agent systems with semi‐Markov switching topologies

This study investigates the leader-following consensus problem for non-linear multi-agent systems with semi-Markov switching topologies. The dynamics of the leader agent and the follower agents is described by a general linear system. Since the transition rates of the semi-Markov switching topologies are time-varying, they are more general and practicable than the classic Markov switching topologies. A novel consensus protocol based on outdated states is proposed for multi-agent systems. By a system transformation, the consensus problem of multi-agent systems is converted into the stability problem of semi-Markov switching systems. The controller design condition is derived utilising the semi-Markov jump system theory and algebraic graph theory, which can guarantee that the multi-agent systems achieve a consensus with an exponential decay rate. A numerical example is given to illustrate the effectiveness of the proposed method.

Sliding mode control for quantized semi-Markovian switching systems with bounded disturbances

Sliding mode control for quantized semi-Markovian switching systems with bounded disturbances

On sliding mode control for networked control systems with semi-Markovian switching and random sensor delays

This paper focuses on the problem of sliding mode control for networked control systems with semi-Markovian switching and random measurement, where the measurement channel is assumed to suffer from random sensor delays. A Luenberger observer is designed to generate the estimation of system states, and the integral sliding surface is constructed to guarantee exponential stability of networked semi-Markovian switching systems in the mean square sense. Then a proper controller is synthesized to ensure that the trajectory of the closed-loop networked semi-Markovian switching systems can be driven onto the prescribed sliding surface. Finally, numerical examples and simulations are provided to illustrate the effectiveness of the integral sliding mode control scheme.

Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching

abstractIn this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system. Existing results for Markovian switching systems may then be applied to analyze phase semi-Markovian switching systems. In the following, we obtain asymptotic stability for the distribution of nonlinear stochastic systems with semi-Markovian switching. The results can also be extended to general semi-Markovian switching systems. Finally, an example is given to illustrate the feasibility and effectiveness of the theoretical results obtained.