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This article investigates the robust exponential stabilization of a class of switched positive systems with uncertainties by co-designing controllers for subsystems and dwell time switching strategy. The uncertainties refer to interval uncertainties. One of the distinguishing features is that none of the forced individual subsystems is assumed to be stabilized. The other feature is that the stabilization for the unforced switched system can not be solvable by designing dwell time switching signal. First, for switched positive systems without uncertainties, a type of multiple time-varying co-positive Lyapunov functions is used, and the computable sufficient conditions on the state feedback controller for each subsystem are derived in the framework of dwell time strategy. Moreover, the exponential stabilization problem is solved by confining the lower and upper bounds of the dwell time, restricting the upper bound of derivative of considered Lyapunov function of the active subsystem, and decreasing the Lyapunov function values at successive switching instants of the overall switched system. Then, the results are extended to the robust exponential stabilization case for switched positive systemswith uncertainties, and sufficient conditions are given in the same framework of the dwell time for that of the forced switched systems by further designing state feedback controllers. Finally, illustration examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

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This paper is concerned with the finite/fixed-time synchronization (FFTS) problems of two delayed memristive reaction–diffusion neural networks (MRDNNs). By designing appropriate state feedback controllers, utilizing the Lyapunov function method and inequality techniques, several sufficient criteria are derived to guarantee the FFTS of the drive-response MRDNNs. Taking into account both the influences of time and space, the model, described as a state-dependent switching system here, is more complex and closer to practical applications than those in the existing results. Finally, an example is presented to substantiate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies finite-time stabilization problem for stochastic low-order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability, combining the Lyapunov function and adding a power integrator technique, and using the stochastic finite-time stability theory, a state feedback controller is designed to guarantee global finite-time stability in probability of stochastic low-order nonlinear systemswith finite-time stochastic input-to-state stability inverse dynamics. [ABSTRACT FROM AUTHOR]

In this study, without assuming the symmetry or irreducibility of the coupling configuration matrix, we investigate the synchronization of linearly coupled dynamical systems with discontinuous identical nodes and time delay. First, we design a feedback controller to realize the complete synchronization and exponential synchronization of discontinuous complex networks using a generalized Lyapunov approach. Second, we propose a set of adaptive controllers and adaptive laws to achieve complete synchronization. Third, we study the adaptive pinning synchronization of the discontinuous complex networks. The results of numerical simulations are presented to demonstrate the effectiveness of the controllers and the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates asymptotic stability in probability and stabilization designs of discrete-time stochastic systems with state-dependent noise perturbations. Our work begins with a lemma on a special discrete-time stochastic system for which almost all of its sample paths starting from a nonzero initial value will never reach the origin subsequently. This motivates us to deal with the asymptotic stability in probability of discrete-time stochastic systems. A stochastic Lyapunov theorem on asymptotic stability in probability is proved by means of the convergence theorem of supermartingale. An example is given to show the difference between asymptotic stability in probability and almost surely asymptotic stability. Based on the stochastic Lyapunov theorem, the problem of asymptotic stabilization for discrete-time stochastic control systems is considered. Some sufficient conditions are proposed and applied for constructing asymptotically stable feedback controllers. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of stability analysis and stabilization with a state feedback controller through pole placement for a class of both continuous and discrete-time switched nonlinear systems. These systems are modeled by differential or difference equations. Then, a transformation under the arrow form is employed. Note that, the main contribution in this work is twofold: firstly, based on the construction of an appropriated common Lyapunov function, as well the use of the vector norms notion, the recourse to the Kotelyanski lemma, the M − m a t r i x proprieties, the aggregation techniques and the application of the Borne–Gentina criterion, new sufficient stability conditions under arbitrary switching for the autonomous system are deduced. Secondly, this result is extended for designing a state feedback controller by using pole assignment control, which guarantee that the corresponding closed-loop system is globally asymptotically stable under arbitrary switching. The main novelties features of these obtained results are the explicitness and the simplicity in their application. Moreover, they allow us to avoid the search of a common Lyapunov function which is a difficult matter. Finally, as validation to stabilize a shunt DC motor under variable mechanical loads is performed to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The underactuated 2-dimensional translational oscillator with rotational actuator (2DTORA) system consisting of an rotational proof-mass and two unactuated translational carts is an extension version TORA which is a well-known benchmark for nonlinear control design. In this paper, dynamics of 2DTORA system is modeled and written in general affine form. And we apply fuzzy Lyapunov synthesis to design a state feedback controller to stabilize the system with partial information about dynamics by using only a linguistic description. The designed state feedback controller is nonlinear which can be simplified as the classic linear state feedback controller. The globally stability of the closed-loop system is proofed according to the second Lyapunov theorem and LaSalle's stability theorem. Simulation results demonstrate the effectiveness of the designed controller and advantages in comparison with a previously designed linear controller for the 2DTORA system. [ABSTRACT FROM AUTHOR]

SUMMARY This paper discusses the exponential stability and stabilization for nonlinear descriptor systems with discrete and distributed delays. In terms of the Lyapunov method, the exponential stability of the slow subsystem is firstly obtained. Then, a new homotopy-based approach is proposed to investigate the exponential stability of the fast subsystem. By an estimate of the weighted matrix norm for a nonlinear mapping, the exponential stability of the fast subsystem and thus delay-dependent sufficient conditions for the exponential stability of the systems are obtained. In addition, a state feedback controller is designed for the stabilization of the nonlinear descriptor systems. Finally, the effectiveness of the proposed approach is illustrated by numerical examples. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A new stochastic switched linear model is established to describe the Zigbee-based wireless networked control system (WNCS) with both network-induced delay and packet dropout. The network-induced delay can be less or longer than one sampling period. A sufficient condition is presented for the exponentially mean square stability of the closed-loop WNCS, and corresponding state feedback controller is designed by using the augmenting technique and multi-Lyapunov approach. Then, combined with carrier sense multiple access with collision avoidance (CSMA-CA) algorithm, a method is given to choose proper parameter values. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]