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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]

Summary: This article deals with the problems of stability and stabilization for a class of discrete‐time switched systems with time‐varying delay under arbitrary switching signal. First, sufficient conditions guaranteeing the asymptotic stability of the unforced system are developed, by using the switched Lyapunov‐Krasovskii functional method. Then, based on the obtained results, a state feedback controller is designed in order to ensure the asymptotic stability of the closed‐loop system. Furthermore, slack variables are introduced for more relaxation. The proposed approach is proved to have some less conservative results than some existing works. Finally, numerical examples are provided to illustrate the effectiveness and the merit of the proposed method and to compare the obtained results with some previous works in the literature. [ABSTRACT FROM AUTHOR]

In this study, combining backstepping sliding mode (BSM) and disturbance observer‐based control (DOBC), a state feedback controller is designed to regulate the speed of induction motor (IM). First, a feedforward compensation method is proposed based on the rotor flux observer and BSM control to counteract the mismatched lumped disturbances. Then, a disturbance observer is established to estimate the overall effect of possible modelling inaccuracy, load disturbance and motor parameters variation in the IM model. Compared with the conventional vector controller, the proposed controller solves the problems of modelling imprecise, unknown load injection and parameter variation, and realises the speed tracking of IM with good performance. Finally, experiments are presented to verify the effectiveness and practicability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This study investigates the impulsive control for the output tracking of probabilistic Boolean control networks (PBCNs) by the algebraic state‐space representation method. Firstly, a novel system with augmented control is established by regarding the impulsive time as a special kind of control, which is equivalent to the considered impulsive PBCN (IPBCN). Secondly, based on the largest control invariant subset, a necessary and sufficient condition is proposed to design impulsive control for the output tracking problem of IPBCNs. Moreover, a constructive method is put forward to design the state feedback controller and state‐dependent impulsive time sequence. Finally, an example is given to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this study, the stabilisation of quasi‐one‐sided Lipschitz non‐linear systems is investigated. For the quasi‐one‐sided Lipschitz non‐linear system, a condition for the existence of the observer is presented. For the weak quasi‐one‐sided Lipschitz non‐linear system, a state feedback controller is proposed and a condition is derived for the existence of the state feedback controller. The separation principle is obtained for the observer‐based controller of the quasi‐one‐sided Lipschitz non‐linear systems. The main results in this study extend and improve those in the literature. Numerical examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

This study investigates the state feedback control laws for Markov jump linear systems with state and mode‐observation delays. An assumption in this study is that the delay of the mode observation obeys an exponential distribution. Also, the authors raise an unknown time‐varying state delay applied in the composition of the state feedback controller. A method of remodelling the closed‐loop system as a standard Markov jump linear system with state delay is shown. Furthermore, on the basis of this remodelling, several linear matrix inequalities for designing feedback gains for stabilisation and mixed H2/H∞ control are proposed. Finally, the authors apply a numerical simulation for examining the effectiveness of the proposed mixed H2/H∞ controller designing method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for eigenvalue assignment using linear control systems containing uncertain elements. Uncertain systems are systems described by state equations which depend on uncertain parameters. In this paper, uncertainty is modeled with interval numbers. The proposed method assigns prescribed eigenvalues to a state feedback control system. Also, we introduce two interval operations to be used in our method use them. Some numerical experiments are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This study proposes a robust tracking controller for an underactuated quadrotor model based on the flatness theory and active disturbance rejection control (ADRC). Exploiting the differential flatness characteristic, it is demonstrated that a non‐linear quadrotor system can be changed into a linear canonical form, where it is easier to create a state feedback controller that ensures accurate trajectory tracking. In order to improve the tracking performance of the quadrotor, other factors are considered in the conception of the state feedback controller consisting in the estimation of the un‐measurable state variables in a canonical (Brunovsky) form and in the elimination of external perturbations and modelling uncertainties affecting the quadrotor system. To deal with this problem, first, an extended state observer (ESO) is designed to estimate a system state and an extended state known as lumped uncertainties. The latter represents the total effects of uncertain parameters, the neglected part of non‐linearity and the external disturbances. Second, based on the ESO result, an additional term is integrated into the feedback controller to eliminate the lumped disturbance effects and to ensure the stability of the closed loop. Simulation results are introduced to prove the benefits of associating the ADRC approach with flatness control. [ABSTRACT FROM AUTHOR]

This study addresses robust QSR‐dissipativity and feedback dissipation of a class of fractional‐order (FO) uncertain linear systems. Both the state and controlled output matrices are with time‐varying norm‐bounded parameter uncertainties. Firstly, some new notions of QSR‐dissipativity and passivity for FO systems are introduced, the relationship between QSR‐dissipativity and asymptotic stability and input–output stability are discussed, respectively. Then, a sufficient condition in the form of linear matrix inequality (LMI) is proposed to ensure that such system is robustly QSR‐dissipative. According to this condition, a state feedback controller is proposed when the full states can be measured. Secondly, by employing LMI techniques and matrices singular value decomposition, sufficient conditions for the existence and a robust dissipation synthesis method are derived, respectively. Thirdly, a design method of dynamic output feedback controller is developed in order to guarantee that the closed‐loop system is dissipative. Finally, some numerical examples are provided to show the application of the proposed methods. [ABSTRACT FROM AUTHOR]

Unlike a general integer‐order linear system, the L1 and L2 norms of its state and output variables may not be convergent in an infinite time interval even if the concerned fractional‐order linear system is asymptotically stable or even Mittag–Leffler stable. Therefore, this study mainly investigates the analysis and synthesis of L1 and L2 performances in a finite time interval for a class of fractional‐order positive systems. The L∞ performance problem in the infinite time interval is also concerned since the boundness of the L∞ norm of the state and output variables can be guaranteed in the infinite time interval if the concerned fractional‐order positive system is asymptotical stable. The L1 and L∞ performance characterisations are expressed by linear programming and L2 performance characterisation is expressed in terms of linear matrix inequality with a diagonal positive definite solution. Based on these performance conditions, the problems of stabilisation by a state feedback controller with Lp(p∈{1,2,∞}) ‐gain guaranteed are solved for fractional‐order positive systems. An example is presented to show the effectiveness of the proposed methods in this study. [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]

This study is concerned about the quantitative exponential stability (QES) and stabilisation of discrete‐time Markov jump systems with multiplicative noises. First, the defects of exponential stability in practical applications are analysed. Based on this analysis, a concept of the QES is given, and two stability criteria are derived. By utilising an auxiliary definition of general finite‐time stability (GFTS), the relations among QES, GFTS and finite‐time stability are established. Moreover, the quantitative exponential stabilisation is studied, and state feedback controller and the observer‐based controller are designed. Subsequently, the relation between the states' upper bound and states' decay rate of considered systems is quantitatively shown by a searching method. Finally, an example is used to illustrate the effectiveness of the authors' obtained results. [ABSTRACT FROM AUTHOR]

This study deals with the observer‐based controller design problem for a class of networked control systems with multirate sampling. A matching mechanism is proposed to synchronise the sampled data between the plant and an observer, and computes the corresponding error. Using the error, the multirate observer is developed to estimate the state of the system in real time. A state feedback controller based on the observer is utilised to control the system. Different from discrete‐time modelling methods, the resulting closed‐loop system is modelled as a continuous‐time system with multiple sawtooth input‐delays. Inspired by Wirtinger's inequality, a new Lyapunov–Krasovskii functional is constructed to analyse efficiently the closed‐loop system in the presence of time‐varying network‐induced delays. Then sufficient conditions for H∞ performance analysis and the observer‐based controller design are presented. Finally, two illustrative examples show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This study investigates the problem of finite‐time stabilisation for a class of switched linear systems with interval time‐varying delay and parametric uncertainties. First, sufficient conditions for the finite‐time stability of unforced switched systems are presented based on the average dwell time method and on the appropriate multiple Lyapunov‐like functions that contain information regarding the lower and upper bounds of delay. A state feedback controller is then proposed for uncertain switched systems, with interval time‐varying delay, which guarantees finite‐time stabilisation of closed‐loop systems. These conditions are formulated using a set of linear matrix inequalities and are dependent on the size of the time delay. Moreover, the criteria obtained are less conservative than some existing results because of the assumption of the upper bound of the derivative of the Lyapunov‐like functions, without the neglect of any useful terms. Finally, two examples are provided to demonstrate the effectiveness of the proposed method. The first is a numerical example, and the second is a practical example involving river pollution control. [ABSTRACT FROM AUTHOR]

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this study, the finite‐time control problem is studied for discrete time‐varying systems with randomly occurring non‐linearity and missing measurements. The randomly occurring non‐linearity is modelled according to a Bernoulli distributed white sequence with a known conditional probability. The missing measurements phenomenon is assumed to occur in a random way and the missing probabilities are time‐varying with known upper and lower bounds. Two sufficient conditions are established for the existence of the state feedback and output feedback controllers, which guarantee the finite‐time stochastic stability of the closed‐loop systems. The recursive linear matrix inequality approach is employed to design the desired controller gains. A numerical example is provided to illustrate the effectiveness of the obtained 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]

SUMMARY An active fault tolerant control (AFTC) method is proposed for discrete-time piecewise affine (PWA) systems. Only actuator faults are considered. The AFTC framework contains a supervisory scheme, which selects a suitable controller in a set of controllers such that the stability and an acceptable performance of the faulty system are held. The design of the supervisory scheme is not considered here. The set of controllers is composed of a normal controller for the fault-free case, an active fault detection and isolation controller for isolation and identification of the faults, and a set of passive fault tolerant controllers (PFTCs) modules designed to be robust against a set of actuator faults. In this research, the piecewise nonlinear model is approximated by a PWA system. The PFTCs are state feedback laws. Each one is robust against a fixed set of actuator faults and is able to track the reference signal while the control inputs are bounded. The PFTC problem is transformed into a feasibility problem of a set of LMIs. The method is applied on a large-scale live-stock ventilation model. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of stabilisation for a class of two‐dimensional (2D) nonlinear systems with intermittent measurements and sector nonlinearities. The intermittent measurement is modelled by a stochastic variable satisfying the Bernoulli random binary distribution. Our attention is focused on the design of a state feedback controller for such 2D stochastic system described by the Roesser model, such that the closed‐loop system is mean‐square asymptotically stable. A sufficient condition is established by means of linear matrix inequalities technique, and formulae can be given for the control law design. The result is also extended to more general cases where the system matrices contain uncertain parameters. Numerical examples are also given to illustrate the effectiveness of proposed approach. [ABSTRACT FROM AUTHOR]

This study is concerned with the passivity and passification problems for Takagi–Sugeno fuzzy descriptor systems subject to stochastic perturbation and time‐varying delay. The stochastic disturbance is given in the form of one‐dimensional Brownian motion and the delay is assumed to be time‐varying and differentiable. By utilising the Lyapunov functional method and the stochastic analysis techniques, a delay‐dependent criterion is presented to ensure that the considered system is regular, impulse‐free, asymptotically stable in the mean‐square sense and passive in the sense of expectation. Then, based on this criterion, two procedures are proposed for designing state‐feedback controller, which guarantee the resulting closed‐loop system admissible and passive in the sense of expectation. All conditions are cast in terms of linear matrix inequalities. Finally, two illustrative examples are given to demonstrate the validity and applicability of the proposed results. [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]

The objective of Muoi et al. 2017 is to give a delay‐dependent criterion for the considered linear singular time‐delay system to be finite‐time stabilisable with a state feedback controller, which is formulated in terms of linear matrix inequalities. However, this criterion is not correct, which is pointed out in this note. [ABSTRACT FROM AUTHOR]