Pingfang Zhou

SMC Design for Robust Stabilization of Nonlinear Markovian Jump Singular Systems

In this technical note, the sliding-mode control (SMC) problem is investigated for T–S fuzzy-model-based nonlinear Markovian jump singular systems subject to matched/unmatched uncertainties. To accommodate the model characteristics of such a hybrid system, a novel integral-type fuzzy sliding surface is put forward by taking the singular matrix and state-dependent projection matrix into account simultaneously, which is the key contribution of the note. The designed surface contains two important features: 1) local input matrices for different subsystems in the same system mode are allowed to be different; and 2) the matched uncertainties are completely compensated, and the unmatched ones are not amplified during sliding motion. Sufficient conditions for the stochastic admissibility of the corresponding sliding-mode dynamics are presented, and a fuzzy SMC law is constructed to ensure the reaching condition despite uncertainties. The applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system.

Robust guaranteed cost control for singular Markovian jump systems with time-varying delay.

This paper is concerned with the guaranteed cost control for continuous-time singular Markovian jump systems with time-varying delay. Without using the free weighting matrices method, a delay-range-dependent condition is derived in terms of strict linear matrix inequality (LMI), which guarantees that the singular system is regular, impulse free and mean-square exponentially stable with an H(∞) performance. Based on this, the existence condition of the guaranteed cost state feedback controller is proposed. A numerical example is given to illustrate the effectiveness and less conservatism of the proposed design method.

Delay-Dependent Passivity and Passification for Uncertain Singularly Perturbed Markovian Jump Systems with Time-Varying Delay

This paper is concerned with passivity analysis and passivity-based controller design for uncertain singularly perturbed Markovian jump systems with time-varying delay in an interval. Firstly, a delay-dependent condition for the considered system to be mean-square exponentially stable and robustly passive is derived in terms of linear matrix inequality. Then, the passification problem is investigated. Based on the obtained passivity condition, the existence of the desired state feedback controller is established. Numerical examples are presented to show the effectiveness of the proposed method.

A new integral sliding mode design method for nonlinear stochastic systems

Abstract Recently, several integral sliding mode control (ISMC) methodologies have been put forward to robust stabilization of nonlinear stochastic systems depicted by T–S fuzzy models. However, these results employ very restrictive assumptions on system matrices, which impose a great limitation to real applications. This paper aims to remove these assumptions and present a new ISMC method for fuzzy stochastic systems subjected to matched/mismatched uncertainties. To this end, a novel fuzzy integral sliding manifold function is adopted such that the matched uncertainties are completely rejected while the mismatched ones will not be enlarged during the sliding mode phase. Sufficient conditions are derived to ensure the stochastic stability of the closed-loop system under sliding motion. A fuzzy sliding mode controller is further presented to maintain the states of fuzzy stochastic system onto the predefined fuzzy manifold in the presence of uncertainties. The effectiveness and benefit of the developed new method are demonstrated by the inverted pendulum system.

Finite time attitude tracking control of an autonomous airship

The problem of station-keeping attitude tracking control for an autonomous airship with system uncertainties and external disturbances is investigated. Adaptive laws are applied to estimate the upper bounds of uncertainties and disturbances, and a nonlinear finite time control scheme is proposed by combing input/output feedback linearization with integral sliding mode technique. Different from the existing works on attitude control of airship, the developed controller can guarantee the yaw, pitch and roll angle trajectories track the desired attitude in finite time in spite of uncertain system uncertainties and external disturbances. Simulation results are provided to illustrate the attitude tracking performance.

Reliable Robust Sampled-Data H∞ Output Tracking Control with Application to Flight Control

This paper is concerned with the problem of robust H ∞ output tracking control for uncertain sampled-data systems with probabilistic actuator failures. By assuming that each actuator fault takes values randomly in a finite set, a new actuator-failure-mode is proposed. Lyapunov-Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach are employed to establish the H ∞ performance, and the controller design is cast into a convex optimization problem with linear matrix inequality (LMI) constraints. The designed reliable controller can guarantee that the output of the closed-loop sampled-data system tracks the reference signal without steady-state error. An airship model is considered in this paper and its simulation results are given. DOI: http://dx.doi.org/10.5755/j01.itc.43.2.4821

State Estimation and Reliable Control of Singular Markovian Systems with Distributed State Delays and Input Delays

This paper is concerned with state estimation and reliable control for singular Markovian jump systems with distributed state delays and input delays. Firstly, an observer is designed to estimate the system states, and a reliable controller is proposed based on the state estimates. Moreover, some conditions for the mean-square exponential admissibility of the overall closed-loop system are derived in terms of strict linear matrix inequality (LMI).

H; ∞ non-fragile observer-based sliding mode control of singular Markovian jump systems with state delay

This paper is concerned with the state estimation and H∞ sliding mode control for delayed singular Markovian jump systems. A non-fragile observer is designed to estimate the system states, and the sliding mode control law is established to ensure the reachability of the sliding surface in the state-estimation space. Then, some sufficient conditions for the stochastic admissibility of the overall closed-loop system with H∞ disturbance attenuation level are derived in terms of strict linear matrix inequality (LMI).

NEW RESULTS ON STABILITY OF STOCHASTIC NEURAL NETWORKS WITH MARKOVIAN SWITCHING AND MODE-DEPENDENT TIME-VARYING DELAYS ∗

This paper is concerned with the problem of exponential stability for a class of stochastic neural networks with Markovian switching and mode-dependent interval time-varying delays. A novel Lyapunov-Krasovskii functional is introduced with the idea of delay-partitioning, and a new exponential stability criterion is derived based on the new functional and free-weighting matrix method. This new criterion proves to be less conservative than the most existing results. Numerical examples are presented to illustrate the effectiveness of the proposed method.

Stability Criteria for Singular Stochastic Hybrid Systems with Mode-Dependent Time-Varying Delay

This paper provides a delay-dependent criterion for a class of singular stochastic hybrid systems with mode-dependent time-varying delay. In order to reduce conservatism, a new Lyapunov-Krasovskii functional is constructed by decomposing the delay interval into multiple subintervals. Based on the new functional, a stability criterion is derived in terms of strict linear matrix inequality (LMI), which guarantees that the considered system is regular, impulse-free, and mean-square exponentially stable. Numerical examples are presented to illustrate the effectiveness of proposed method.