New gain-scheduling control conditions for time-varying delayed LPV systems

This paper investigates the problem of stability and state-feedback control design for linear parameter-varying systems with time-varying delays. The uncertain parameters are assumed to belong to a polytope with bounded known variation rates. The new conditions are based on the Lyapunov theory and are expressed through Linear Matrix Inequalities. An alternative parameter-dependent Lyapunov-Krasovskii functional is employed and its time-derivative is handled using recent integral inequalities for quadratic functions proposed in the literature. As main results, a novel sufficient stability condition for delay-dependent systems as well as a new sufficient condition to design gain-scheduled state-feedback controllers are stated. In the new proposed methodology, the Lyapunov matrices and the system matrices are put separated making it suitable for supporting in a new way the design of the stabilization controller. An example, based on a model of a real-world problem, is provided to illustrate the effectiveness of the proposed method.     

Cascading state-space decomposition of Boolean control networks by nested method

Boolean control networks are a kind of discrete logical dynamical systems. They are recently attracting considerable interest as computational models for genetic and cellular networks. In this paper, we investigate the cascading state-space decomposition problem for Boolean control networks by nested method. Firstly, based on the semi-tensor product of matrices, we obtain some algebraic conditions for the cascading state-space decomposition. Secondly, the multi-layer nested block matrix is defined, and two necessary and sufficient conditions are put forward based on this kind of matrices. Besides, a method is given to design controllers. Finally, an example is given to display the effectiveness of the method provided in this paper.     

Constrained model predictive fault-tolerant control for multi-time-delayed batch processes with disturbances: A Lyapunov-Razumikhin function method

This paper mainly studies the design of iterative learning constrained model predictive fault–tolerant control for batch processes accompanied by multi–delays, interference and actuator failures. Firstly, an equivalent 2D–Roesser model with multi–delays is established. The definition of invariant set is proposed. The sufficient conditions with invariant set characteristics are established. After that the predictive fault-tolerant controller is designed with terminal constraints against external disturbances. In this paper, Lyapunov–Razumikhin Function (LRF) is used to form Lyapunov–Krasovskii Function (LKF) to construct the sufficient condition for the predictive control system that satisfies the terminal constraint condition. Moreover, the system state still remains invariant set characteristics. This method has certain advantages in controller design and calculation. In addition, it has the characteristics of simple design and small computation, and is especially suitable for small delay systems. Finally, a simulation experiment in the nonlinear batch reactor is carried out. Compared with the traditional one-dimensional (1D) method, the presented strategy has better performance through simulation experiment.     

Passive fuzzy controller design for nonlinear systems with multiplicative noises

This paper proposes a passive fuzzy controller design methodology for nonlinear system with multiplicative noises. Applying the Itô's formula and the sense of mean square, the sufficient conditions are developed to analyze the stability and to design the controller for stochastic nonlinear systems which are represented by the Takagi-Sugeno (T-S) fuzzy models. The sufficient conditions derived in this paper belong to the Linear Matrix Inequality (LMI) forms which can be solved by the convex optimal programming algorithm. Besides, the passivity theory is applied to discuss the effect of external disturbance on system. Finally, some numerical simulation examples are provided to demonstrate the applications of the proposed fuzzy controller design technique.     

Quadratic stability analysis and robust distributed controllers design for uncertain spatially interconnected systems

This paper is concerned with the quadratic stability analysis and robust distributed controllers design of both continuous-time and discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). The well-posedness, quadratic stability, and contractiveness of USISs are properly defined for the first time. A sufficient condition employing the given system matrices is established to check the well-posedness, quadratic stability and contractiveness. This condition is simpler than the existing conditions based on the decomposition of system matrices. Based on the new condition derived, a sufficient condition is given for the existence of robust distributed controllers and a constructive method is then presented for the design of robust distributed controllers. The advantage of the proposed constructive approach is that it employs the given system matrices while the existing methods conduct the bilinear transformation on these matrices when design controllers, and consequently, the constructive approach in this paper is computationally more efficient than the existing methods. Several examples are included to demonstrate the simplicity, efficiency and applicability of the derived theoretical results.     

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.     

Asymptotic stability of general linear dynamical networks under distributed relative-state feedback control

This paper investigates general linear dynamical networks (GLDNs), distributed relative-state feedback control, and pinning control. For symmetric GLDNs under distributed relative-state feedback control, some necessary and sufficient conditions for asymptotic stability are proposed. While for the asymmetric case, some sufficient conditions are derived. If the obtained stability conditions are not satisfied, one can design some pinning controllers to asymptotically stabilize the GLDNs. Compared with the existing results, the considered dynamical network model is more general, and the obtained theoretical results are novel.     

Predefined-time tracking of nonlinear strict-feedback systems with time-varying output constraints

In this paper, the problem of the predefined-time tracking with time-varying output constraints (TVOC) is investigated for a class of nonlinear strict-feedback systems. First, the sufficient conditions for the studied problem are presented. Then, a recursive design algorithm of the controller is proposed by backstepping technique. A novel stabilizing function is constructed by adding a fractional term, which is capable of decreasing the asymmetric time-varying Barrier Lyapunov Function (BLF) to the origin within any desired settling time. After that, it is shown that under our proposed control, all the closed-loop signals are bounded, and the tracking error converges to zero within any desired settling time and remains zero thereafter without the violation of the output constraint. The settling time in this paper is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Finally, two examples are given to illustrate the effectiveness of the proposed method.     

Dissipative output feedback control for semi-Markovian jump systems under hybrid cyber-attacks

In this paper, the dissipativity-based dynamic output feedback controller (DOFC) design for Semi-Markovian jump systems under stochastic cyber-attacks is first proposed. It is assumed that the time-varying uncertainties obey Bernoulli-distribution and transition probability matrix is time-varying and partially accessed. By utilizing the dissipativity-based technique, sufficient conditions for the existence of the DOFC are obtained to ensure the exponential stability with a strict dissipative performance of the resulted system. Next, the proposed results are improved by fractionalizing the time-varying transition probability matrix and the corresponding DOFC gains are obtained by cone complementarity linearization algorithm. Simulations results are provided to demonstrate the effectiveness and theoretical value of the proposed dissipativity-based DOFC design method.     

Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay

The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-term approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.     

Sufficient conditions for simultaneous stabilization of three linear systems within the framework of nest algebras

In this paper, we study the problem of the simultaneous stabilization of three time-varying discrete-time linear systems within the framework of nest algebras. From the perspective of strong transitivity, we establish sufficient condition for the existence of time-varying simultaneously stabilizing controllers based on the coprime factorization. In particular, we also derive a sufficient condition for simultaneous stabilizability of three systems, where the systems are pairwise simultaneously stabilizable. Additionally, the sufficient conditions given in this paper lead to a constructive controller design to stabilize simultaneously three systems. These results hold as well in the time-invariant case. Two examples are included for illustration.     

一类线性切换系统的鲁棒跟踪控制

文章研究了线性切换系统的鲁棒跟踪控制,并提出可解性的充分条件。设计切换控制规则使得切换线性系统满足加权H∞参考模型,并采用平均驻留时间法和Lyapunov函数来处理稳定性分析和控制器设计。通过使用线性矩阵不等式,控制器设计问题可以得到很好的解决。     

Finite-time robust control of a class of nonlinear time-delay systems via Lyapunov functional method

This paper investigates the finite-time robust control problem of a class of nonlinear time-delay systems with general form, and proposes some new delay-independent and delay-dependent conditions on the issue. First, by developing an equivalent form, the paper studies finite-time stabilization problem, and presents some delay-dependent stabilization results by constructing suitable Lyapunov functionals. Then, based on the stabilization results, we study the finite-time robust control problem for the systems, and give a robust control design procedure. Finally, the study of two illustrative examples shows that the results obtained of the paper work well in the finite-time stabilization and robust stabilization for the systems. It is shown that, by using the method in the paper, the obtained results do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden. Moreover, different from existing finite-time results, the paper also presents delay-dependent sufficient conditions on the finite-time control problem for the systems.     

State estimation for semi-Markovian switching CVNNs with quantization effects and linear fractional uncertainties

This paper is concerned with the robust state estimation problem for semi-Markovian switching complex-valued neural networks with quantization effects (QEs). The uncertain parameters are described by the linear fractional uncertainties (LFUs). To enhance the channel utilization and save the communication resources, the measured output is quantized before transmission by a logarithmic quantizer. The purpose of the problem under consideration is to design a full-order state estimator to estimate the complex-valued neuron states. Based on the Lyapunov stability theory, stochastic analysis method, and some improved integral inequalities, sufficient conditions are first derived to guarantee the estimation error system to be globally asymptotically stable in the mean square. Then, the desired state estimator can be directly designed after solving a set of matrix inequalities, which is robust against the LFUs and the QEs. In the end of the paper, one numerical example is provided to illustrate the feasibility and effectiveness of the proposed estimation design scheme.     

Probability-constrained tracking control for a class of time-varying nonlinear stochastic systems

This paper is concerned with the probability-constrained tracking control problem for a class of time-varying systems with stochastic nonlinearities, stochastic noises and successively packet loss. The main purpose of this paper is to design a time-varying observer and tracking controller such that (1) the probabilities of both the estimation error and tracking error confined to given ellipsoidal sets are larger than prescribed constants, and (2) the ellipsoids are minimized in the sense of matrix norm at each time point. By using a stochastic analysis method, the probability constrained tracking control problem is solved and sufficient conditions are obtained in terms of recursive linear matrix inequalities. A recursive optimization algorithm is developed to design the observer and tracking controller such that not only the addressed probability constrained aim is satisfied, but also the ellipsoidal sets are minimized. At last, a simulation example is given to illustrate the effectiveness and applicability of the developed approach.     

Exponential stabilization and sampled-date H∞ control for uncertain T–S fuzzy systems with time-varying delay

In this paper, the exponential stabilization problem of uncertain T–S fuzzy systems with time-varying delay is emulated by fuzzy sampled-data H_∞ control. Firstly, a novel suitable Lyapunov–Krasovskii function is constructed, which contains all the information about the sampling pattern. Secondly, a less conservative result is achieved by using an extended Jensen inequality, and purposefully using a compact free weighting matrix. In addition, according to the linear matrix inequality (LMI), some sampled-data H_∞ exponential stability sufficient conditions and controller design of T–S fuzzy systems are established. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.     

TS fuzzy robust L1 control for nonlinear systems with persistent bounded disturbances

In this paper, a novel technique for Takagi–Sugeno (TS) model-based robust L₁ controller design of nonlinear systems is proposed. Two synthesis methods based on quadratic and non-quadratic Lyapunov functions are considered. To design the robust stabilizing controller, a new approach for deriving sufficient conditions associated with the L₁ performance criterion in terms of strict linear matrix inequality is proposed. This novel technique results in less pre-chosen scalar design variables and calculation burden. Furthermore, deriving the controller synthesis conditions via a non-quadratic Lyapunov function (NQLF) relaxes the obtained conditions. Therefore, the proposed approaches not only efficiently minimize the effect of persistent bounded disturbance, but also are applicable for wider classes of TS systems. Furthermore, some new lemmas are proposed to facilitate strict LMI formulation and to provide more degrees of freedom. Finally, several numerical and practical examples are presented to show the merits of this paper.     

Average consensus in networks of dynamic agents with uncertain topologies and time-varying delays

In this paper, we study average consensus problem in networks of dynamic agents with uncertain topologies as well as time-varying communication delays. By using the linear matrix inequality method, we establish several sufficient conditions for average consensus in the existence of both uncertainties and delays. Several linear matrix inequality conditions are presented to determine the allowable upper bounds of time-varying communication delays and uncertainties. Numerical examples are worked out to illustrate the theoretical results.     

Finite-time stabilization of nonlinear time delay systems using LQR based sliding mode control

In this paper, we discussed the robust finite-time stability of conic type nonlinear systems with time varying delays. Some novel conditions are derived to design a linear quadratic regulator (LQR) based sliding mode control (SMC) by proposing an integral switching surface. The sufficient conditions are derived for the considered nonlinear system using Lyapunov–Krasovskii stability theory and linear matrix inequality (LMI) approach. The proposed conditions can be solved using some standard numerical packages. Finally, a practical example is provided to validate the advantages and effectiveness of the proposed results.