Free-weighting Approach Research Articles

Robust $$ H_{\infty } $$ Fault-Tolerant Control for Discrete-Time Nonlinear System with Actuator Faults and Time-Varying Delays Using Nonlinear T–S Fuzzy Models

In this paper, the problem of fault estimation and fault-tolerant control for a class of nonlinear discrete-time system state time-varying delay and actuator fault is investigated. This class of systems is represented through the Takagi–Sugeno (T–S) fuzzy model with nonlinear functions satisfying some sector-bounded conditions. By adding these nonlinear functions in the local sub-models, the observer and controller can be designed with fewer rules and less computation burden. The method proceeds in two steps: first, a full-order fuzzy fault estimation observer (FFEO) design is proposed to estimate the actuator faults and the nonlinear functions in the T–S models. Second, based on the online fault estimation, a dynamic output feedback fault-tolerant controller (DOFTC) is then designed to compensate the effect of faults by stabilizing the closed-loop system. Furthermore, sufficient less conservative delay-dependent conditions for the existence of the desired FFEO and DOFTC are given in terms of linear matrix inequalities by employing the fuzzy Lyapunov–Krasovskii function and free-weighting approach. Finally, a practical example is given to show the effectiveness and advantages of the proposed approach.

Partial-information-based consensus of network systems with time-varying delay via sampled-data control

In this paper, a novel decoupling method is introduced to investigate the consensus of network systems with partial coupling on the basis of sampling control. The novel method is enabled us to discuss channels of each node for network systems individually. By constructing several Lyapunov functionals and combining with free weighting approach, the stability of network systems with target node is analyzed. On the other hand, network systems with time-varying delay are considered. Based on Fourier theory, an alternative inequality is presented, which is more precise than the Wirtinger inequalities. This inequality encompasses the Jensen one and leads to manageable linear matrix inequalities conditions (LMIs). Therefore, the consensus of network systems with time-varying delay can be guaranteed. Through two illustrated examples, the effectiveness of the proposed method is demonstrated sufficiently.

Efficient Approach to Stability Analysis of Discrete-Time Systems with Time-Varying Delay

This paper aims at deriving an efficient criterion for the robust stability analysis of discrete-time systems with time-varying delay. In the derivation, to obtain a larger stability region under the requirement of less computational complexity, this paper proposes a valuable method capable of establishing a less conservative stability criterion without using the free-weighting approach and an extremely augmented state. In parallel, the stabilization problem of systems with time-delayed control input is addressed in connection with the derived stability criterion.