Asynchronous input-output finite-time filtering for switched LPV systems

The input-output finite-time filtering problem is addressed for a class of switched linear parameter-varying systems in this paper. Firstly, by constructing a parameter-dependent Lyapunov function and resorting to the average dwell time approach, sufficient conditions ensuring finite-time boundedness and input-output finite-time stability are established for the augmented filtering error system. Then, a parameter-dependent asynchronous filter is designed such that the augmented filtering error system are both finite-time bounded and input-output finite-time stable. Finally, the active magnetic bearing model is introduced and verifies the main algorithms in this paper.     

Enhanced stability criteria of neural networks with time-varying delays via a generalized free-weighting matrix integral inequality

This paper deals with the problem of delay-dependent stability analysis for neural networks with time-varying delays. First, by constructing an augmented Lyapunov–Krasovskii functional and utilizing a generalized free-weighting matrix integral inequality, an improved stability criterion for the concerned network is derived in terms of linear matrix inequalities. Second, by considering a marginal augmented vector and modifying a Lyapunov–Krasovsii functional, a further enhanced stability criterion is presented. Third, a less conservative stability condition in which a relaxed inequality related to activation functions is added is introduced. Finally, three numerical examples are included to illustrate the advantage and validity of the proposed criteria.     

Stochastic stability and extended dissipativity analysis for delayed neural networks with markovian jump via novel integral inequality

This paper studies the stochastic stability and extended dissipativity analysis for delayed Markovian jump neural networks (MJNNs) with partly unknown transition rates (PUTRs) using novel integral inequality. A new double integral inequality with augmented vector is introduced through inequality technique and the zero-valued equality approach, which can more efficiently estimate the derivative of the triple integral inequality. Next, an augmented Lyapunov-Krasovskii functional (LKF) with delay-product-type (DPT) is constructed. Besides, with the introduced integral inequality, the augmented LKF and some other analytical techniques, some less conservative extended dissipation conditions are obtained in the form of linear matrix inequality (LMI). Finally, several examples are provided to illustrate the effectiveness of the obtained results.     

Stability analysis for systems with multiple/single time delays via a Cascade augmented L-K functional

This paper investigates stability of linear systems with multiple/single time-delays. Firstly, a three-level cascade augmented Lyapunov-Krasovskii (L-K) functional is introduced, in which interconnect information among delayed state vectors is fully taken into account. Based on a newly integral inequality and the cascade L-K functional, a novel stability criterion is derived for linear systems with multiple time-delays. Secondly, it is found that the proposed L-K functional is also suitable for linear systems with single time-delay if the delay-partitioning method is employed. This motivates us to obtain a less conservative stability condition for linear systems with single time-delay. Finally, Numerical examples are given to confirm the advantages of the proposed method.     

An event-triggered model predictive control with exponentially stable offset free for PWA systems with model-plant mismatch

A new event-triggered model predictive control (MPC) method is proposed for PWA systems with model-plant mismatch, such that, for a given asymptotically constant reference signal, exponential stability and unbiased tracking can be achieved. Firstly, for the PWA system, an observer is designed to estimate state and the model-plant mismatch. To guarantee the exponential stability, an event is introduced, and an event-triggered model predictive controller is designed as well. By introducing state error and estimate error, an augmented model is constructed. Then, using the model-dependent average dwell time (MDADT) method and Lyapunov stability theory, exponentially stable condition of the closed-loop system is derived, which is formulated by linear matrix inequalities (LMIs), and zero offset is also guaranteed under some mild assumptions. Moreover, the MDADT of each sub-system is given simultaneously. Finally, simulations have been taken to verify the effectiveness of the proposed method.     

Some augmented approaches to the improved stability criteria for linear systems with time-varying delays

This work investigates the improved stability conditions for linear systems with time-varying delays via various augmented approaches. Some augmented approaches are augmented Lyapunov-Krasovskii functionals, augmented zero equalities, and the augmented zero equality approach. At first, by constructing augmented Lyapunov-Krasovskii functionals including the state vectors which were not considered in the previous works and augmented zero equalities, a stability criterion is proposed in the forms of linear matrix inequalities. Through the proposed Lyapunov-Krasovskii functionals and an additional functional derived from the integral inequality, a slightly improved result is derived. The proposed results do not consider the increase in the computational complexity to achieve a larger delay bound. So, by applying the augmented zero equality approach, which is a method of grafting the proposed augmented zero equality proposed in Finsler Lemma, to the proposed result, an enhanced stability result was derived. Also, the computational complexity is reduced by appropriately adjusting any vector of the integral inequality utilized in the proposed criteria. By applying some numerical examples to the proposed conditions, the effectiveness and superiority of the results are confirmed.     

Network-based PI control for output tracking of continuous-time systems with time-varying sampling and network-induced delays

For a continuous-time linear system with constant reference input, the network-based proportional-integral (PI) control is developed to solve the output tracking control problem by taking time-varying sampling and network-induced delays into account. A traditional PI control system is introduced to obtain the equilibriums of state and control input. Using the equilibriums, a discrete-time PI tracking controller in a network environment is constructed. The resulting network-based PI control system is described by an augmented system with two input delays and the output tracking objective is transformed into ensuring asymptotic stability of the augmented system. A delay-dependent stability condition is established by a discontinuous augmented Lyapunov–Krasovskii functional approach. The PI controller design result of in-wheel motor as a case study is provided in terms of linear matrix inequalities. Matlab simulation and experimental results resorting to a test-bed for ZigBee-based control of in-wheel motor are given to validate the proposed method.     

Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality

In this paper, the problem of stability analysis for linear systems with time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via three numerical examples by the comparison of maximum delay bounds.     

Improved results on stability analysis of time-varying delay systems via delay partitioning method and Finsler’s lemma

This paper proposes novel conditions based on linear matrix inequalities (LMI) for stability analysis of arbitrarily-fast time-varying delays systems. The time-varying delay interval is divided into smaller pieces in order to obtain an equivalent switched model with multiple time-varying delays of smaller interval, which differently from other existing approaches, the maximum switching frequency is not required for stability analysis. Thus, by the use of augmented Lyapunov-Krasovskii functionals and the Finsler’s lemma, together with some relationships among state variables intentionally defined, the inherent conservatism can be progressively reduced by refining more and more the delay partition. The superiority of the proposed method is illustrated through two benchmark examples.     

Dynamic output feedback sliding mode control for spacecraft hovering without velocity measurements

In consideration of target angular velocity uncertainty and external disturbance, a modified dynamic output feedback sliding mode control (DOFSMC) method is proposed for spacecraft autonomous hovering system without velocity measurements. As a stepping-stone, an additional dynamic compensator is introduced into the design of sliding surface, then an augmented system is reconstructed with the system uncertainty and external disturbance. Based on the linear matrix inequality (LMI), a sufficient condition is given, which guarantees the disturbance attenuation performance of sliding mode dynamics. By introducing an auxiliary variable, a modified version of adaptive sliding mode control (ASMC) law is designed, and the finite-time stability of sliding variable is established by the Lyapunov stability theory. Compared with other results, the proposed method is less conservative and can decrease the generated control input force significantly. Finally, two simulation examples are performed to validate the effectiveness of the proposed method.     

New results on stability analysis of systems with time-varying delays using a generalized free-matrix-based inequality

This paper addresses the delay-dependent stability problem of linear systems with interval time-varying delays. A generalized free-matrix-based inequality is proposed and employed to derive stability conditions, which are less conservative than the Bessel–Legendre inequality. An augmented Lyapunov–Krasovskii functional is tailored for the generalized free-matrix-based inequality. Then, some items in the Lyapunov–Krasovskii functionals are integrated so as to relax its positive definite condition, which provides a more accurate lower bound for the Lyapunov–Krasovskii functionals. Therefore, some less conservative stability criteria are presented. Two numerical examples illustrate the effectiveness of the method.     

Improved approaches to stability criteria for neural networks with time-varying delays

In this paper, the problem of stability analysis for neural networks with time-varying delays is considered. By the use of a newly augmented Lyapunov functional and some novel techniques, sufficient conditions to guarantee the asymptotic stability of the concerned networks are established in terms of linear matrix inequalities (LMIs). Three numerical examples are given to show the improved stability region of the proposed works.     

基于区间时变时滞模糊系统的稳定性分析

考虑了区间时变时滞模糊系统的稳定性问题.利用T-S模糊模型对模糊系统进行了研究,利用线性矩阵不等式的形式给出了此类模糊系统在时滞相关意义下保守性更小的稳定性判据.由于加入了自由矩阵,所得结果保守性更小.并且给出了一个数值例子说明了所得稳定性判据的有效性.     

Observer-based output feedback control for networked systems with dual-channel event-triggered sampling and quantization

This paper investigates the problem of observer-based output feedback control for linear networked systems with dual-channel event-triggered mechanisms and quantization. Both continuous-time and discrete-time event detection cases are discussed. In the continuous-time case, the stability of observer error dynamics and closed-loop system are analyzed respectively, and it is proved that Zeno behavior would not occur. In order to approach engineering practice, in the discrete-time case, two types of network attacks including denial-of-service (DoS) and fault data injection (FDI) attacks are considered, whose nature property is characterized by Bernoulli variables. By combining these factors and transmission delay, a novel augmented system model is proposed, and some sufficient conditions are derived based on Lyapunov functional approach and linear matrix inequalities (LMIs). Compared with the existing results, this framework is more comprehensive and practical, and the global uniform ultimate boundedness of closed-loop systems can be guaranteed. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method.     

Synchronization for chaotic systems via mixed-objective dynamic output feedback robust model predictive control

This paper focuses on mixed-objective dynamic output feedback robust model predictive control (OFRMPC) for the synchronization of two identical discrete-time chaotic systems with polytopic uncertainties, energy bounded disturbances, and input constraint. Using active control strategy, the chaos synchronization is transformed into standard dynamic OFRMPC scenarios tractable through receding horizon min–max optimization. Utilizing the notion of quadratic boundedness, the augmented closed-loop stability is further characterized. Then, the concepts of mixed performance criteria are firstly incorporated into the dynamic OFRMPC scheme to guarantee both the robust stability and the disturbance attenuation ability while preserving better dynamical behaviors. Necessary and/or sufficient conditions for desired mixed-objective dynamic OFRMPC are formulated involving linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the theoretical results.     

Stability analysis of sampled-data systems considering time delays and its application to electric power markets

This paper investigates the stability of linear control systems with aperiodic sampled data and communication delays. A systematic analysis method is presented and then it is applied to an electric power market. Firstly, the sampled-data system is transformed into a system with a special time-varying delay via the input delay method. Secondly, a less conservative stability criterion is derived based on Lyapunov theory. Several augmented terms and an extra integral term are introduced during the constructing of candidate Lyapunov–Krasovskii functional (LKF); and an improved free-weighting matrix approach is used to handle with the LKF itself and its derivative for obtaining the relaxed conditions ensuring the positive and decreasing requirements of the LKF. The benefit of those treatments on the conservativeness-reducing is analyzed and verified based on a simple numerical example. Finally, the application of the proposed method to a simplified electric power market is investigated, including modeling the system with market clearing time and communication delay, and determining the stability region. The application also shows the practical significance of the reducing of the conservativeness.     

Stochastic stabilization of Markovian jump neutral systems with fractional Brownian motion and quantized controller

This paper explores the delay dependent stochastic stabilization of Markovian jump neutral systems (MJNS) which are modeled by fractional Brownian motion(fBm) via a quantized controller. A function Round quantizer is introduced which solves the model uncertainties and the nonlinear part by a uniform operator. Then by structuring a Lyapunov–Krasovskii functional (LKF) and the aid of linear matrix inequalities (LMIs) method, a stochastic stability criterion is achieved. Last, different parameters are selected to simulate the effectiveness of our findings.     

Observer-based exponential stabilization for time-delay systems via augmented weighted integral inequality

In this paper, we design observer-based feedback control for a class of linear systems. The novelty of the paper comes from the consideration of an augmented weighted based integral inequality involving quadratic functions with an exponential term which is less conservative than the celebrated weighted integral inequality employed in the context of time-delay systems. By using appropriately chosen Lyapunov–Krasovskii functional (LKF), together with the derived integral inequality, a new sufficient condition for exponential stability in terms of linear matrix inequalities (LMIs) is proposed for the delayed linear systems with state feedback control. Finally, the applicability and superiority of the proposed theoretical results over the existing ones are analyzed in virtue of numerical examples.     

Security control for networked control systems with randomly occurring integrity check protection subject to randomly occurring zero-value attacks

This paper investigates the problem of secure control for networked control systems (NCSs) under randomly occurring zero-value attacks (ROZVAs). Specifically, ROZVAs only offset the true signal without injecting obfuscated information or noises, and possess the minimum energy of the added malicious information. To protect system stability against ROZVA, randomly occurring integrity check protection (ROICP) is introduced which prevents malicious data injection with less energy cost than persistently occurring protection. Besides the random phenomena of ROZVA and ROICP, which are characterized by two mutually independent random variables obeying the Bernoulli distribution, the randomly occurring time delays caused by ROICP are also considered in system modelling. According to the built stochastic linear system model, security analysis of the NCS with ROICP subject to ROZVA is carried out and sufficient condition for stochastic stability is derived via a linear matrix inequality (LMI) approach. Based on the proposed condition, a compensation feedback controller is designed to facilitate system stability. Finally, simulation results show the effectiveness of the proposed method.     

Reachable set estimation for linear systems with time-varying delay and polytopic uncertainties

This study is concerned with the problem of reachable set estimation for linear systems with time-varying delays and polytopic parameter uncertainties. Our target is to find an ellipsoid that contains the state trajectory of linear system as small as possible. Specifically, first, in order to utilize more information about the state variables, the RSE problem for time-delay systems is solved based on an augmented Lyapunov-Krasovskii functional. Second, by dividing the time-varying delay into two non-uniformly subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. Third, the integral interval is decomposed in the same way to estimate the bounds of integral terms more exactly. Fourth, an optimized integral inequality is used to deal with the integral terms, which is based on distinguished Wirtinger integral inequality and Reciprocally convex combination inequality. This can be regard as a new method in the delay systems. Finally, three numerical examples are presented to demonstrate the effectiveness and merits of the theoretical results.