New results on reachable sets bounding for delayed positive singular systems with bounded disturbances

This paper addresses the reachable sets bounding problem for time-delay positive singular systems subject to bounded disturbances. The time delays in the considered systems are assumed to be time-varying. Both invariant and time-varying singular systems are investigated in this paper. Existence conditions of componentwise ultimate bounds of the state vector of considered systems are derived and given in terms of the spectral abscissa of the system matrices, which are easy to be checked. The obtained results are demonstrated by two numerical examples.     

Sliding manifold design for linear systems with unmatched disturbances

This paper offers an efficient sliding manifold design method that minimizes the impact of unmatched disturbances onto SM dynamics and system accuracy. System sensitivity upon unmatched constant or slowly varying external disturbance vector is evaluated by the steady-state dependent criterion function. An infinite set of sliding manifolds that minimize the chosen optimization criterion is determined and a way of selecting a manifold out of that set that provides adopted SM dynamics is suggested. The proposed approach has been demonstrated on numerical examples and verified by simulations.     

Dynamics of linear delayed systems with decaying disturbances

Dynamical systems in the real world are always subject to various disturbances. This paper studies the dynamics of linear delayed systems with decaying disturbances, both discrete- and continuous-time cases are considered. It is first shown that if an unforced linear system is exponentially stable, then the disturbed system has a dynamical property like exponential stability provided that the disturbance decays at an exponential rate, and has a dynamical property like asymptotic stability provided that the disturbance asymptotically approaches zero. These results are then applied to block triangular systems in the presence of time-varying delays, leading to criteria for checking the stability properties of this class of systems by considering diagonal blocks of system matrices. Particularly, a block triangular system is exponentially stable if and only if each system described by the diagonal blocks of system matrices is exponentially stable. Finally, a numerical example is presented to illustrate the theoretical results.     

A delay-dependent stability criterion for linear neutral delay systems

A new stability criterion for linear neutral delay systems is developed in this note. Based on Park's inequality, a new delay-dependent stability criterion is derived. A numerical example is proposed to illustrate the less conservatism of the obtained results.     

Distributed disturbance observer based consensus control for linear multi-agent systems with mismatched disturbances

This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws.     

On linear generalized neutral differential delay systems

In this paper, the class of linear generalized neutral differential delay systems with time-invariant coefficients is studied. These kinds of systems are inherent in many physical and engineering phenomena. Using the matrix pencil theory, we decompose it into five subsystems, whose solutions are obtained. Moreover, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable.     

Necessary conditions for exponential stability of linear neutral type systems with multiple time delays

In this paper, we will give necessary conditions for the exponential stability of linear neutral type systems with multiple time delays by employing the Lyapunov–Krasovskii functional approach. These conditions not only extend the existing results of the neutral-delay-free systems, but also provide a new tool for stability analysis of linear neutral type systems with multiple time delays by characterizing instability domains. As a medium step, we will investigate several crucial properties which are involved with both the fundamental matrix and Lyapunov matrix. Numerical examples illustrate the validity of the theoretical results.     

Output reachable set estimation for discrete-time switched systems with persistent dwell-time

This paper is concerned with the output reachable set estimation for discrete-time switched systems. The switching signal is considered as persistent dwell-time (PDT), which is more general and flexible compared with the common dwell-time and average dwell-time switching. The estimation of output reachable set is determined by a collection of bounding ellipsoids based on a family of quasi-time-dependent (QTD) Lyapunov functions. Furthermore, a set of non-fragile QTD controllers is designed. Finally, two examples are employed to illustrate the potentials of proposed methods.     

Further results on asymptotic stability of linear neutral systems with multiple delays

The problem of asymptotic stability of linear neutral systems with multiple delays is addressed in this article. Using the characteristic equation approach, new delay-independent stability criteria are derived in terms of the spectral radius of modulus matrices. The structure information of the system matrices are taken into consideration in the proposed stability criteria, thus the conservatism found in the literature can be significantly reduced. Simple examples are given to demonstrate the validity of the criteria proposed and to compare them with the existing ones.     

A further note on stability criterion of linear neutral delay-differential systems

This paper is a further note which corrects an error of the paper by Park and Won. A new stability criteria which is less conservative than those in the literature is presented.     

A necessary and sufficient condition for delay-independent stability of linear time-varying neutral delay systems

In this paper, stability analysis of linear time-varying neutral delay systems is considered. A necessary and sufficient condition for delay-independent global asymptotic stability of such systems is derived. Eventually, two examples are given in order to show the results established.     

Full-order and reduced-order observers for linear parameter-varying systems with one-sided Lipschitz nonlinearities and disturbances using parameter-dependent Lyapunov function

In this study, H_∞ full-order and reduced-order observers are designed for a class of linear parameter-varying (LPV) systems with one-sided Lipschitz nonlinearities and disturbances. Parameter-dependent Lyapunov function is used to analyze the robust stability of the proposed observers. Three practical examples are used to demonstrate the usefulness of the proposed observers. Simulation and experimental results indicate that the proposed observers work well.     

Convergent under-approximations of reachable sets and tubes: A piecewise constant approach

In this paper, a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems is proposed. The class under consideration is the linear time-varying (LTV) class with time-varying integrable system matrices and uncertain initial and input values belonging to known convex compact sets. The proposed method depends upon the iterative use of constant-input reachable sets, which results in convergent under-approximations in the sense of the Hausdorff distance. As a consequence of the convergence, it is shown that interior points of reachable sets are attainable using piecewise constant inputs. The computational complexity of a zonotopic implementation of the proposed method is discussed and comparisons with existing under-approximation methods are established. Finally, the proposed approach is illustrated through two numerical examples.     

Scale-based cluster formation for multi-agent systems with mismatched disturbances

This paper studies scale-based cluster formation problem of multi-agent system (MASs) under mismatched disturbances. A distributed sliding mode control with a disturbance observer is proposed to solve the aforementioned problem in the leaderless and leader-follower cases. The proposed control strategy provides satisfactory robust performance under mismatched disturbances and is thus more applicable to complicated formation control tasks. Finally, simulation results are provided to justify the validity of the proposed method.     

Event-triggered stabilisation for stochastic delayed differential systems with exogenous disturbances

In this paper, the practically input-to-state stabilization issue is considered for the stochastic delayed differential systems (SDDSs) with exogenous disturbances. To reduce the transmission frequency of the feedback control signal, the proposed SDDSs are stabilized by an event-triggered strategy. The concept of the practically input-to-state stability (ISS) is used to describe the dynamic performance of control target in the event-triggered schemes and exogenous disturbances. Besides, the considered SDDSs is stabilized by an event-triggered feedback controller which is represented by linear matrix inequalities. Moreover, lower bound of the interaction time of the event-triggered control method is obtained to avoid the Zeno behavior of the proposed event-triggering scheme. Finally, the effectiveness of the conclusion is verified by a numerical example.     

Continuous fixed-time convergent regulator for dynamic systems with unbounded disturbances

This paper presents a novel continuous fixed-time convergent control law for dynamic systems in the presence of unbounded disturbances. A continuous fixed-time convergent control is designed to drive all states of a multi-dimensional integrator chain at the origin for a finite pre-established (fixed) time, using a scalar input. The fixed-time convergence is established and the uniform upper bound of the settling time is computed. The designed control algorithm is applied to fixed-time stabilization of two mechatronic systems, a cart inverted pendulum and a single machine infinite bus turbo generator with main steam valve control.