Exponential stability of impulsive systems with random delays under sampled‐data control

This paper investigates the exponential stabilisation problem of nonlinear impulsive systems with complex delays, in which both system and impulse delays are permitted to exceed impulse intervals. These complex delays induce intricate dependencies between system states and control actions, significantly increasing difficulty in deriving sufficient conditions for global exponential stability (GES). To tackle this challenge, a novel interval partitioning analysis method is presented. It establishes a quantifiable relationship between impulse delay, impulse interval, and system state. Building on this relationship, a new Razumikhin inequality is designed, leveraging the influence of impulse delay on system stability and eliminating the constraints between impulse and system delays. By using the average dwell time (ADT) criterion, a sufficient stability condition expressed as Linear Matrix Inequalities (LMIs) is derived. It is shown that under specific conditions on the historical state feedback and impulse sequence, the delayed impulse system exhibits exponential stability, even with variable impulse intervals. Two numerical examples demonstrate the effectiveness of the presented method, showcasing its applicability to image encryption.

This paper focuses on the issue of robustly exponential stability for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations. Some new sufficient conditions dependent on the delays are derived in terms of Lyapunov-Krasovskii functionals combined with free-weighting matrices. Two numerical examples are given to show the effectiveness of the proposed method.

A new robust stability criterion is developed to guarantee the stability of the feedback systems subjected to noises and nonlinear time-varying plant perturbations. The main contribution of this paper is an extension of the results of robust stability for the class of feedback systems containing nonlinear time-varying plant perturbations to the class of systems with unstable plants and noises. The generally parameterized stabilizing controller, advanced by Youla et al., is combined with Schur function (class S) to synthesize the robust stabilizers of the feedback systems subjected to noises and nonlinear time-varying plant perturbations.

SummaryThis note is concerned with the linear estimation problems for discrete‐time systems where the measurements are subject to random time delay and packet dropout. Different from most of previous works, the time‐stamping is assumed to be unavailable in this paper. In this case, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time‐stamping, a new observation is introduced by the summation of all the measurements received in the same time. Then, the random time delay measurement system is converted into a constant‐delay measurement system with multiplicative noises where the noise is binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by using the transformation of auto‐regressive moving average model to state‐space model and the standard Kalman filtering. The convergence and stability of the filter are also analyzed. A simulation example is given to show the effectiveness of the proposed estimator. Copyright © 2016 John Wiley & Sons, Ltd.

This note is concerned with the linear estimation problems for discrete-time systems where the measurements are subject to random time delay and packet drop. Due to the time stamping being assumed to be unavailable in this paper, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time-stamping, a new observation is defined by the summation of all the measurements received in the same time. Then the random time delay measurement system is converted into a constant-delay measurement system with multiplicative noises by using binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by combining the transformation of ARMA model to state-space model and the standard Kalman filtering. A simulation example is given to show the effectiveness of the proposed estimator.

Reliable control for networked control systems with probabilistic actuator fault and random delays

The decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem is investigated for a class of continuous-time large-scale networked nonlinear systems with interconnection. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi–Sugeno model and is closed by a communication channel with transformed time delay. Our objective is to design a decentralized sampled-data fuzzy controller such that the resulting fuzzy control system is asymptotically stable with an \({\mathscr{H}}_{\infty }\) performance. Firstly, using an input delay approach, the sampled-data control system is formulated into the system with time-varying delay, and a two-term approximation method is proposed such that the delayed system is reformulated into an interconnected framework with input and output. Then, we introduce a Lyapunov–Krasovskii functional that all Lyapunov matrices are no longer required to be positive definite. Combined with the scaled small gain theorem, the less conservative solutions to the decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem for the considered system are derived in the form of linear matrix inequalities. Finally, the effectiveness of the proposed methods is illustrated by two numerical examples.

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

The use of avionics networks for flight control system has reduced aircraft weight, system installation, integration and maintenance costs as well as introduced time delays and structured uncertainties. This paper studies the robust stability and stabilisation problem of uncertain networked flight control system with random time delays. Some new sufficient criteria with simple mathematical forms for robust stability and stabilisation of networked flight control system are derived by a free weighting matrix approach. A memoryless state feedback robust controller and the maximum bound of time delay are obtained based on the solution of linear matrix inequalities (LMIs) which are established by the Lyapunov-Krasovskii stability theory. Numerical examples are given to illustrate the effectiveness of design procedure.

This paper is concerned with the delay-dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations. By proposing a new Lyapunov-Krasovskii (L-K) functional which contains some triple integral terms, combined with integral inequalities and free-weighting matrix technique, a neutral and discrete delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs). This criterion enlarges the upper bound of the time-delay and has less conservative. Numerical examples are given to demonstrate the effectiveness of the proposed stability criterion.

Stability of stochastic time-delay systems involving delayed impulses

In order to solve the potential issues caused by network induced delays and dropouts which could arise the performance degradation and system instability, this paper studies the stochastic stability problem of Networked control systems (NCSs) with arbitrary time delays and packet dropouts by using an active time-varying sampling method. The random time delays and successive packet dropouts are driven by two separately Markov chains and NCSs are modelled as a discrete time Markovian jump linear systems. Based on Lyapunov approach, sufficient conditions for the stochastic stability of the networked control system are derived and stabilization controller is designed in terms of linear matrix inequalities (LMIs) correspondingly. Gridding approach is introduced to guarantee the solvability of the LMIs with finite jump modes. A numerical example is given to illustrate the effectiveness of the proposed method which stabilizes the NCS with random time delays and packet dropouts.

In this paper, the problem of an exponential stability for time-delay systems with interval time-varying delays and nonlinear perturbations is investigated. Based on the Lyapunov method, a new delay-dependent criterion for exponential stability is established in terms of LMI (linear matrix inequalities). Numerical examples are carried out to support the effectiveness of our results.

The sampled-data synchronization problem for complex networks with random coupling strengths, probabilistic time-varying coupling delay, and distributed delay (mixed delays) is investigated. The sampling period is assumed to be time varying and bounded. By using the properties of random variables and input delay approach, new synchronization error dynamics are constructed. Based on the delay decomposition method and reciprocally convex approach, a delay-dependent mean square synchronization condition is established in terms of linear matrix inequalities (LMIs). According to the proposed condition, an explicit expression for a set of desired sampled-data controllers can be achieved by solving LMIs. Numerical examples are given to demonstrate the effectiveness of the theoretical results.

A refined input delay approach to sampled-data control