Fanbiao Li

State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties

This paper is concerned with the state estimation and sliding mode control problems for phase-type semi-Markovian jump systems. Using a supplementary variable technique and a plant transformation, a finite phase-type semi-Markov process has been transformed into a finite Markov chain, which is called its associated Markov chain. As a result, phase-type semi-Markovian jump systems can be equivalently expressed as its associated Markovian jump systems. A sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated Markovian jump systems satisfy the reaching condition. Moreover, an observer-based sliding mode control problem is investigated. Sufficient conditions are established for the solvability of the desired observer. Two numerical examples are presented to show the effectiveness of the proposed design techniques.

Fuzzy-model-based D-stability and nonfragile control for discrete-time descriptor systems with multiple delays

This paper is concerned with the problems of D-stability and nonfragile control for a class of discrete-time descriptor Takagi-Sugeno (T-S) fuzzy systems with multiple state delays. D-stability criteria are proposed to ensure that all the poles of the descriptor T-S fuzzy system are located within a disk contained in the unit circle. Furthermore, a sufficient condition is presented such that the closed-loop system is regular, causal, and D-stable, in spite of parameter uncertainties and multiple state delays. The corresponding solvability conditions for the desired fuzzy-rule-dependent nonfragile controllers are also established. Finally, examples are given to show the effectiveness and advantages of the proposed techniques.

Quantized Control Design for Cognitive Radio Networks Modeled as Nonlinear Semi-Markovian Jump Systems

This paper is concerned with the quantized control design problem for a class of semi-Markovian jump systems with repeated scalar nonlinearities. A semi-Markovian system of this kind has been transformed into an associated Markovian system via a supplementary variable technique and a plant transformation. A sufficient condition for associated Markovian jump systems is developed. This condition guarantees that the corresponding closed-loop systems are stochastically stable and have a prescribed H∞ performance. The existence conditions for full- and reduced-order dynamic output feedback controllers are proposed, and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one, which can be solved efficiently with existing optimization techniques. Finally, an application to cognitive-radio systems demonstrates the efficiency of the new design method developed.

Neural Network-Based Passive Filtering for Delayed Neutral-Type Semi-Markovian Jump Systems

This paper investigates the problem of exponential passive filtering for a class of stochastic neutral-type neural networks with both semi-Markovian jump parameters and mixed time delays. Our aim is to estimate the states by designing a Luenberger-type observer, such that the filter error dynamics are mean-square exponentially stable with an expected decay rate and an attenuation level. Sufficient conditions for the existence of passive filters are obtained, and a convex optimization algorithm for the filter design is given. In addition, a cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem, which can be readily solved by the existing optimization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed techniques.

Dissipativity-Based Filtering for Fuzzy Switched Systems With Stochastic Perturbation

In this technical note, the problem of the dissipativity-based filtering problem is considered for a class of T-S fuzzy switched systems with stochastic perturbation. Firstly, a sufficient condition of strict dissipativity performance is given to guarantee the mean-square exponential stability for the concerned T-S fuzzy switched system. Then, our attention is focused on the design of a filter to the T-S fuzzy switched system with Brownian motion. By combining the average dwell time technique with the piecewise Lyapunov function technique, the desired fuzzy filters are designed that guarantee the filter error dynamic system to be mean-square exponential stable with a strictly dissipative performance, and the corresponding solvability condition for the fuzzy filter is also presented based on the linearization procedure approach. Finally, an example is provided to illustrate the effectiveness of the proposed dissipativity-based filter technique.

Fault Detection Filtering for Nonhomogeneous Markovian Jump Systems via a Fuzzy Approach

This paper investigates the problem of the fault detection filter design for nonhomogeneous Markovian jump systems by a Takagi–Sugeno fuzzy approach. Attention is focused on the construction of a fault detection filter to ensure the estimation error dynamic stochastically stable, and the prescribed performance requirement can be satisfied. The designed fuzzy model-based fault detection filter can guarantee the sensitivity of the residual signal to faults and the robustness of the external disturbances. By using the cone complementarity linearization algorithm, the existence conditions for the design of fault detection filters are provided. Meanwhile, the error between the residual signal and the fault signal is made as small as possible. Finally, a practical application is given to illustrate the effectiveness of the proposed technique.

Nonfragile Output Tracking Control of Hypersonic Air-Breathing Vehicles With an LPV Model

This paper presents a novel nonfragile output tracking control scheme for flexible hypersonic air-breathing vehicles (HAVs). This problem is challenging due to the complex interactions between the aerodynamics, the propulsion system, and the structural dynamics. By utilizing the curve-fit and the least-squares methods, a new model for HAVs is established, and then converted into a linear parameter-varying system, in which the scheduling variables depend on a handful of meaningful states and parameters. With a specified reference model, a tracking error model is also proposed. The nonfragile output tracking controller is designed, which guarantees the tracking error dynamics to be robustly stable. Finally, simulation results are presented to show the effectiveness of the proposed control design scheme.

Passivity-Based Asynchronous Sliding Mode Control for Delayed Singular Markovian Jump Systems

This paper is concerned with the problem of passivity-based asynchronous sliding mode control for a class of uncertain singular Markovian jump systems with time delay and nonlinear perturbations. The asynchronous control strategy is employed due to the nonsynchronization between the controller and the system modes. Considering the singularity of the system, a novel integral-type sliding surface is constructed, and then the asynchronous sliding controller is synthesized to ensure that the sliding mode dynamics satisfy the reaching condition. Sufficient conditions are presented such that the corresponding sliding mode dynamics are admissible and robustly passive. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed technique.

Event-Based Fault Detection Filtering for Complex Networked Jump Systems

This paper is concerned with the fault detection filtering for complex systems over communication networks subject to nonhomogeneous Markovian parameters. A residual signal is generated that gives a satisfactory estimation of the fault, and an event-triggered scheme is proposed to determine whether the networks should be updated at the trigger instants decided by the event-threshold. Moreover, a random process is employed to model the phenomenon of malicious packet losses. Consequently, a novel method is presented to address the stochastically stability analysis and satisfies a given

Fault Detection for Underactuated Manipulators Modeled by Markovian Jump Systems

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