Delay-independent stability conditions for a class of nonlinear difference systems

The paper addresses the asymptotic stability problem for a class of difference systems with nonlinearities of a sector type and time-delay. A new approach to Lyapunov–Krasovskii functionals constructing for considered systems is proposed. On the basis of the approach, delay-independent asymptotic stability conditions and estimates of the convergence rate of solutions are derived. In addition, stability of perturbed systems is investigated in the case where nonstationary perturbations admit zero mean values. Some examples are given to illustrate the obtained results.     

A simplified stability test for 1-D discrete systems

This paper shows that the stability tests for 1-D discrete systems using the transformation p=(z+z⁻¹) and properties of Chebyshev polynomials developed previously can be directly obtained from the z-domain continued fraction expansion based on the functions (z+1) and (z⁻¹+1) on an alternate basis. Furthermore, it is shown that the root distribution of a polynomial with real coefficient can be determined by the same algorithm.     

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.     

Observer-based sliding mode control for a class of discrete systems via delta operator approach

In this paper, an observer-based sliding mode control (SMC) problem is investigated for a class of uncertain delta operator systems with nonlinear exogenous disturbance. A novel robust stability condition is obtained for a sliding mode dynamics by using Lyapunov theory in delta domain. Based on a designed sliding mode observer, a sliding mode controller is synthesized by employing SMC theory combined with reaching law technique. The robust asymptotical stability problem is also discussed for the closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the developed method.     

Consensus stability of a class of second-order multi-agent systems with nonuniform time-delays

This paper is concerned with a consensus problem of a class of second-order multi-agent systems with nonuniform time-delays. A distributed consensus algorithm is adopted to drive all agents to reach consensus and move together with a constant velocity. By a frequency domain approach, an upper bound on the maximum of the time-delays that can be tolerated is given for the consensus of the system.     

Exponential stability and stabilization of a class of uncertain linear time-delay systems

This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov-Krasovskii functional combined with Leibniz-Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities (LMIs), which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples.     

Observer design and stability analysis for a class of PDE chaotic systems

This paper deals with observer design and stability for a class of partial differential equation (PDE) systems governed by one-dimensional wave equations with mixed derivative terms and superlinear boundary conditions, whose dynamics exhibits chaos when the system parameters change within certain ranges. Firstly, a sufficient and necessary condition that guarantees the stability of this class of systems is obtained. Secondly, based on the method of characteristics, an observer is designed by injecting the measurement output estimation error on the boundary, and the observation error dynamics is proved to be stable with a necessary and sufficient criterion, which can identity the range of the feedback gain for the observer. Finally, two numerical examples are provided to illustrate the validity of the theoretical conclusions.     

An embedding approach to the stability of some nonlinear discrete systems

An embedding approach is proposed to investigate the stability of some nonlinear sampled data systems. It is shown that the stability criterion so obtained may conclude for stability when other criteria do not apply. The approach could be extended in a more general way.     

Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems

In this paper, the issues of finite-time extended dissipative analysis and non-fragile control are investigated for a class of uncertain discrete time switched linear systems. Based on average dwell-time approach, sufficient conditions for the finite-time boundedness and finite-time extended dissipative performance of the considered systems are proposed by solving some linear matrix inequalities, where using the concept of extended dissipative, we can solve the H_∞, $L_2?L_{\infty },$ Passivity and (Q, S, R)-dissipativity performance in a unified framework. Furthermore, two form of non-fragile state feedback controllers are designed to guarantee that the closed-loop systems satisfy the finite-time extended dissipative performance. Finally, simulation example is given to show the efficiency of the proposed methods.     

A reset observer with discrete/continuous measurements for a class of fuzzy nonlinear systems

This paper proposes the design of a reset fuzzy observer for the class of nonlinear systems able to be described by a Takagi–Sugeno fuzzy model. The observer uses both continuous and discrete measurements and in contrast with the observers based on the First Order Reset Element (FORE), it updates its states resetting the initial condition of the integrator at each instant when the discrete measurements are available. The proposed fuzzy observer is applied to estimate the substrate and biomass concentration of an anaerobic wastewater treatment process and the effectiveness of the proposed method is tested by simulations comparing the results of a reset fuzzy observer with two fuzzy observers using continuous measurements only. Finally, the estimation scheme is validated using experimental data from an actual anaerobic digestion process, suggesting that the proposed reset fuzzy observer is a practical and encouraging approach to the state estimation of the class nonlinear processes under study.     

Exponential stability of a class of nonlinear singularly perturbed systems with delayed impulses

A class of nonlinear singularly perturbed systems with delayed impulses is considered. By delayed impulses we mean that the impulse maps describing the state's jumping at impulsive moments are dependent on delayed state variables. Assuming that each of two lower order subsystems possesses a Lyapunov function, exponential stability criteria for all small enough values of singular perturbation parameter are obtained. It turns out that the achieved exponential stability is robust with respect to small impulse input delays. A stability bound on perturbation parameter is also derived through using those Lyapunov functions. Additionally, for a class of singularly perturbed Lur'e systems with delayed impulses, an LMI-based method to determine stability and an upper bound of the singular perturbation parameter is presented. The results are illustrated by an example for the position control of a dc-motor with unmodelled dynamics.     

Robust stability analysis for a class of fractional order systems with uncertain parameters

The research of robust stability for fractional order linear time-invariant (FO-LTI) interval systems with uncertain parameters has become a hot issue. In this paper, it is the first time to consider robust stability of uncertain parameters FO-LTI interval systems, which have deterministic linear coupling relationship between fractional order and other model parameters. Linear matrix inequalities (LMI) methods are used, and a criterion for checking asymptotical stability of this class of systems is presented. One numerical illustrative example is given to verify the correctness of the conclusions.     

New results on BIBO stability analysis for a class of neutral delay systems

This paper studies bounded input bounded output (BIBO) stability for a class of neutral systems with time-varying delays. Based on Lyapunov method and linear matrix inequalities, some new BIBO stability criteria are established. The numerical simulation is made to demonstrate the effectiveness of the theoretical results obtained in this paper.     

On consistency of linear linearly constrained discrete time systems

This paper addresses the problem of giving consistency conditions for constrained linear discrete time systems in state space form. Conditions for various significant cases are given and analysed. Finally, the structure of the set of initial states for which consistency prevails and the set of reachable states are studied.     

On the excitability of a class of positive continuous time-delay systems

This article is on the excitability of positive linear time-invariant systems subject to internal point delays. It is proved that excitability independent of delay is guaranteed if an auxiliary delay-free system is excitable. Necessary and sufficient conditions for excitability and transparency independent of the delay size are formulated in terms of the parameterization of the dynamics and control matrices. Some particular results are also given for the properties being dependent on the size of the point delay and for any possible finite values of the delay. The same formulation is given in parallel in terms of strict positivity of a matrix of an associate system obtained from the influence graph of the original system. The excitability and transparency properties are both testable through simple algebraic tests involving a moderate computational effort that is directly related to the system's order.     

On input-to-state stability of impulsive stochastic systems

This paper is concerned with the input-to-state stability (ISS) of impulsive stochastic systems. First, appropriate concepts of stochastic input-to-state stability (SISS) and pth moment input-to-state stability (p-ISS) for the mentioned systems are introduced. Then, we prove that impulsive stochastic systems possessing SISS-Lyapunov functions are uniformly SISS and p-ISS over a certain class of impulse sequences. As a byproduct, a criterion on the uniform global asymptotic stability in probability for the system in isolation (without inputs) is also derived. Finally, we provide a numerical example to illustrate our results.     

A necessary and sufficient condition for stability of linear discrete systems with parameter-variation

A simple sufficient stability criterion for linear discrete systems obtained previously is proved to be necessary and sufficient for the stability of a class of such systems with parameter-variation.     

On delay-dependent robust stability of a class of uncertain mixed neutral and Lur’e dynamical systems with interval time-varying delays

This paper deals with the problem of a new delay-dependent robust stability criteria for a class of mixed neutral and Lur’e systems. The system has time-varying uncertainties, interval time-varying delays and sector-bounded nonlinearity. The proposed method is based on Lyapunov method, a delay-dependent criterion for asymptotic stability is established in terms of linear matrix inequality (LMI). Numerical examples show the effectiveness of the proposed method.     

Necessary conditions of exponential stability for a class of linear uncertain systems with a single constant delay

In this paper, we will investigate the necessary conditions, described by the Lyapunov matrix, for the robust exponential stability for a class of linear uncertain systems with a single constant delay and time-invariant parametric uncertainties, which are some generalizations of the existing results on uncertain linear time-delay systems. As a medium step, several pivotal properties of parameter-dependent Lyapunov matrix are proposed, which set up the relationships between fundamental matrix and Lyapunov matrix for the considered system. In addition, to calculate the parameter-dependent Lyapunov matrix, we introduce the differential equation method and the Lagrange interpolation method, respectively. Furthermore, it is noted that the proposed necessary conditions can be used to estimate the range of time delay, when the linear uncertain time-delay system is robust exponential stability. Finally, the validity of the obtained theoretical results is illustrated via numerical examples.     

Exponential stability analysis for a class of neutral singular Markovian jump systems with time-varying delays

This paper deals with the exponential stability problem for a class of neutral singular systems with Markovian jump parameters. The considered systems involve time-varying delays not only in their state but also in their derivatives of state. By using the Lyapunov–Krasovskii functional method, some sufficient conditions are derived, which ensure that the considered systems are regular, impulse-free and exponentially stable. Finally, some numerical examples are employed to demonstrate the effectiveness of the obtained approaches.