For mechanical systems using displacement measurements only, this study presents a dynamic compensator-based second-order sliding mode control algorithm without using any observer structure to estimate the velocity. Introducing the compensator into the sliding variable, a modified asymptotically stable second-order sliding mode control is developed. The proposed low-order dynamic controller inherently has low-pass filter property in which the effect of differentiators can be obtained. Using singular perturbation theory, the authors show that the system state is finally constrained in a small bound region when the gain is high enough. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.

The problems of finite-time boundedness (FTB) and stabilisation for a class of non-linear quadratic time-delay systems with exogenous disturbances are investigated in this study. Based on the quadratic Lyapunov function, Razumikhin-type techniques, and a particular presentation for the quadratic terms, sufficient conditions for FTB and stabilisation for quadratic systems with exogenous disturbances are derived in terms of linear matrix inequalities. Simulation examples are given to verify the effectiveness of the methodology proposed in this study.

In this study, the authors formulate and study the distributed formation problem of multi-agent systems (MASs) with randomly switching topologies and time-varying delays. The non-linear dynamics of each agent at different time intervals corresponds to different switching mode, and the switching design reflects the changing of travelling path in practical systems. The communication topology of the system switches among finite modes that are governed by a finite-state Markov process. On the basis of artificial potential functions, a formation controller is designed in a general form. Sufficient conditions for stochastic formation stability of the MAS are obtained in terms of a Lyapunov functional and linear matrix inequalities. Some heuristic rules to design a formation controller for the MAS are then presented. Finally, specific potential functions are discussed and corresponding simulation results are provided to demonstrate the effectiveness of the proposed approach.

This study addresses the robust stabilisation problem for the two-dimensional (2D) discrete non-linear stochastic systems with time-varying delays in states. Based on the well-known Fornasini–Marchesini local state-space model, a more general 2D discrete non-linear system is considered with both stochastic disturbances and time-varying delays. Our attention is focused on the design of a delay-dependent state-feedback controller so that the 2D stochastic non-linear system is guaranteed to be globally asymptotically stabilisable in the mean square. By using the stochastic analysis and some inequality techniques, sufficient criteria ensuring the existence of such controllers are derived in terms of matrix inequalities, which can be effectively solved by resorting to some standard convex optimisation algorithms. Furthermore, such stabilisation results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. Finally, a numerical example is provided to demonstrate the applicability of the proposed controller design approach.

This study is concerned with the passivity and passification problems for Takagi–Sugeno fuzzy descriptor systems subject to stochastic perturbation and time-varying delay. The stochastic disturbance is given in the form of one-dimensional Brownian motion and the delay is assumed to be time-varying and differentiable. By utilising the Lyapunov functional method and the stochastic analysis techniques, a delay-dependent criterion is presented to ensure that the considered system is regular, impulse-free, asymptotically stable in the mean-square sense and passive in the sense of expectation. Then, based on this criterion, two procedures are proposed for designing state-feedback controller, which guarantee the resulting closed-loop system admissible and passive in the sense of expectation. All conditions are cast in terms of linear matrix inequalities. Finally, two illustrative examples are given to demonstrate the validity and applicability of the proposed results.

Based on a method of network split according to the different nature of time-delay, the model of the united directed complex networks with multi-links are established. The exponential synchronisation of this model via adaptive periodically intermittent control is further investigated in this study. Via the Lyapunov stability theory combined with the method of the adaptive control, pinning control and periodically intermittent control, some novel and simple criteria are derived for the global exponential synchronisation of the complex dynamical networks with multi-links, and the derived results are less conservative. Several corresponding adaptive feedback synchronisation controllers, pinning controllers and impulsive controllers are designed, respectively. The restriction on the control width and the time delay are removed. This leads to a larger application scope for this method. Using chaotic system as the nodes of the networks, some numerical examples of the united directed complex networks with multi-links and delayed complex networks are given to demonstrate the effectiveness of the control strategies, respectively.

Under the weaker condition on the system non-linearities, this study investigates the problem of global stabilisation by state feedback for a class of high-order non-linear systems with time-varying delays. By using the method of adding a power integrator, a continuous state-feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov–Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.

This study presents a stability condition for a guaranteed cost sampled-data fuzzy control problem of non-linear systems. A Takagi–Sugeno (T–S) fuzzy model is adopted for the non-linear system and the sampled-data fuzzy controller is designed for a T–S fuzzy system. To develop the guaranteed cost control, a new stability condition of the closed-loop system is guaranteed in the continuous-time Lyapunov sense, and its sufficient conditions are formulated in terms of linear matrix inequalities. Based on the stability condition, the guaranteed cost control is considered and minimised for the closed-loop system from the continuous-time cost function. Finally, numerical examples are provided to verify the effectiveness of the proposed technique.

In this study, the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic linear system with mixed time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii functional and utilising a convex polyhedron method, some new delay-dependent exponential stability criteria for such system are established in forms of linear matrix inequalities, which have less conservatism. Finally, three illustrative numerical examples are given to show the effectiveness of the obtained results.

The paper proposed an adaptive filter for jump Markov systems with unknown measurement noise covariance. The filter is derived by treating covariance as a random matrix and an inverse-Wishart distribution is adopted as the conjugate prior. The variational Bayesian approximation method is employed to derive mode-conditioned estimates and mode-likelihood functions in the framework of interacting multiple model. A numerical example is provided to illustrate the performance of the proposed filter.