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Summary: This paper concentrates on strong delay‐independent stability of neutral linear time‐invariant delay systems with multiple commensurate time delays. The stability analysis of linear neutral systems is complicated by the need to locate the roots of a transcendental characteristic equation and to take into account the global hyperbolicity of an associated difference system. In this paper, we propose a convex necessary and sufficient condition for testing strong delay‐independent stability. This result mainly follows from Kronecker sum properties and the Kalman‐Yakubovich‐Popov lemma, which allows us to present the main result in terms of a single linear matrix inequality feasibility test. The paper is closed by showing numerical examples that illustrate the applicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a novel perspective on fully distributed adaptive protocol design for bipartite consensus under directed communication graphs. It is revealed that the fully distributed protocol is indeed a PI‐gain design approach. Based on such PI‐gain method, fully distributed observer‐based protocols are proposed to solve the consensus problem of nonlinear multi‐agent systems over directed cooperative‐antagonistic networks, where the neural network approximation is introduced to tackle the unknown nonlinearity. Fully distributed continuous protocols are further presented by modifying the sign function with a decaying variable, which takes the advantage of avoiding chattering problem. Theoretical analysis and numerical simulations are given to support our main results. [ABSTRACT FROM AUTHOR]

Summary: This paper concerns the analysis of an iterative scheme delivering approximate control laws for the tracking regulation problems for nonlinear systems. The procedure can be applied to finite‐ and infinite‐dimensional systems, and the underlying methodology derives from the geometric methods, which have been developed for both linear and nonlinear systems. In the nonlinear case, the main tool is the center manifold theorem. Indeed, in the geometric methodology, under the assumption that the signals to be tracked are generated by a finite‐dimensional exo‐system, the desired control is obtained by solving a pair of operator equations called the regulator equations. In this paper, we extend the concept of regulator equations to what we refer to as the dynamic regulator equations. Just as it is generally quite difficult to solve the regulator equations, it can be equally difficult to solve the dynamic regulator equations. As the authors have already shown in the linear case, a straightforward attempt to solve the dynamic regulator equations leads to a singular system, which can be regularized to obtain an iterative scheme that provides approximate control laws that provide accurate tracking with very a small tracking error after only a couple of iterations. In this paper, we generalize the iterative scheme to nonlinear systems and provide error estimates for the first 3 iterations. Both finite‐ and infinite‐dimensional examples are given to validate the estimates. We comment that the method has also been applied to a wide range of nonlinear distributed parameter examples described in the references. [ABSTRACT FROM AUTHOR]

In this paper, output regulation for linear delta operator systems subject to actuator saturation is investigated by state feedback. The relation between the regulatable regions and the null controllable region is described in this paper. A set of all initial conditions of a plant and a exosystem is called asymptotically regulatable region for which output regulation is possible. An asymptotically regulatable region is characterized according to a null controllable region of an anti-stable subsystem of the plant. Feedback laws are constructed to solve the problems on output regulation. A numerical example is given to illustrate the effectiveness and potential for the developed techniques. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Traditionally, an anti-windup compensator is activated when control signal saturation occurs. An alternative approach is to activate the compensator at a level below that of the physical control constraints: the anti-windup compensator is activated in anticipation of actuator saturation. Recent studies have proposed systematic methods for the construction of such anticipatory anti-windup compensators, but a pseudo-LPV representation of the saturated system has been central to these results. This paper approaches the anticipatory anti-windup problem for open-loop stable plants using a 'non-square' sector condition, which is associated with a combination of deadzone nonlinearities. The advantage of this approach is that it leads to synthesis routines, which bear a close resemblance to those associated with traditional immediately activated anti-windup compensators. A by-product of this approach also appears to be that the arising compensators are better numerically conditioned. Some simulation examples illustrating the effectiveness of anticipatory anti-windup compensators and some comments on their wider use complete the paper. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the issue of output feedback finite‐time stabilization is investigated for a class of p‐norm stochastic systems with output constraints. A novel tan‐type barrier Lyapunov function (BLF) is constructed to cope with the constraint on the system output, and a finite‐time state feedback controller is subsequently designed by the adding a power integrator technique. Then, based on the designed state feedback controller and a devised nonsmooth observer for the unmeasurable state, the output feedback finite‐time stabilizer is obtained. Both the theoretical analysis and numerical example demonstrate that the proposed scheme guarantees the finite‐time stability of the considered system without violating the prespecified output constraint. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a continuous‐time optimization method for an unknown convex function restricted to a dynamic plant with an available output including a stochastic noise. For solving the problem, we propose an extremum seeking algorithm based on a modified synchronous detection method for computing a stochastic gradient descent approach. In order to reject from the beginning the undesirable uncertainties and perturbations of the dynamic plant, we employ the standard deterministic integral sliding mode control transforming the initial dynamic plant to the static one, and after (in fact, from the beginning of the process), we apply the gradient decedent technique. We consider time‐decreasing parameters for compensating the stochastic dynamics. We prove the stability and the mean‐square convergence of the method. To validate the exposition, we perform a numerical example simulation. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are proposed to the finite‐time stability of the system with the fractional order. Numerical results are given and compared with other published data in the literature to demonstrate the validity of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper presents sufficient conditions to ensure the exponential stability of uncertain switched time‐delay systems with time‐delayed state‐dependent switching conditions, which can model high speed supercavitation vehicles (HSSVs). Based on the intrinsic properties of HSSVs, cavity can be represented by a relation between the states and time‐delayed states of the system. Moreover, a sliding behavior can be occurred at the cavity boundary in HSSVs. Therefore, the main contribution of this paper is to develop a set of LMI stability conditions in the presence of time‐delayed states in the linear state‐dependent switching signal and absorbing sliding modes in the state space, simultaneously. In addition, because of the possible existing uncertainties in HSSVs, another set of LMI‐based sufficient conditions is derived in order to analyze the stability of switched time‐delay systems with additive norm bounded uncertainties. The application of the proposed theorems are also validated through numerical examples. Finally, the stability of a two‐degrees‐of‐freedom longitudinal description of an HSSV is shown using the proposed stability theorems. [ABSTRACT FROM AUTHOR]

Summary: The research on discrete‐time higher‐order sliding mode has received a considerable attention recently. Systems with unmatched uncertainties are common in practice; however, the existing discrete‐time higher‐order sliding mode control algorithms are designed considering only matched uncertainty. This paper proposes a technique to design discrete‐time higher‐order sliding mode control for an uncertain LTI system in the presence of unmatched uncertainty. The proposed technique is numerically simulated and experimentally validated on an electromechanical rectilinear plant. Various experiments are conducted considering the several operational conditions of electromechanical systems in industries to verify the performance of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper studies the partial consensus problem for identical feedforward dynamic systems with input saturations. We construct two consensus protocols using the partial-state information and full-state information, respectively. Applying a change of coordinates, feedforward system is transformed into the block diagonal form. Then, by utilizing the bounded real lemma and small gain theorem, we solve the partial consensus problem, and the existence of each protocol is derived. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new model reference control architecture to effectively suppress system uncertainties and achieve a guaranteed transient and steady-state system performance. Unlike traditional robust control frameworks, only a parameterization of the system uncertainty given by unknown weights with known conservative bounds is needed to stabilize uncertain dynamical systems with predictable system performance. In addition, the proposed architecture's performance is not dependent on the level of conservatism of the bounds of system uncertainty. Following the same train of thought as adaptive controllers that modify a given reference system to improve system performance, the proposed method is inspired by a recently developed command governor theory that minimizes the effect of system uncertainty by augmenting the input signal of the uncertain dynamical and reference systems. Specifically, a dynamical system, called a command governor, is designed such that its output is used to modify the input of both the controlled uncertain dynamical and reference systems. It is theoretically shown that if the command governor design parameter is judiciously selected, then the controlled system approximates the given original, unmodified reference system. The proposed approach is advantageous over model reference adaptive control approaches because linearity of the uncertain dynamical system is preserved through linear control laws, and hence, the closed-loop performance is predictable for different command spectrums. Additionally, it is shown that the architecture can be modified for robustness improvements with respect to high frequency content due to, for example, measurement noise. Modifications can also be made in order to accommodate actuator dynamics and retain closed-loop stability and predictable performance. The main contribution of this paper is the rigorous analysis of the stability and performance of a system utilizing the command governor framework. A numerical example is provided to illustrate the effectiveness of the proposed architecture. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a continuous-time O( n)-constrained Kalman-like filter. O( n) is the group of n × n orthonormal matrices. The O( n)-constrained Kalman-like filter is derived by posing a constrained optimization problem. The solution involves a projection of the unconstrained Kalman state estimate derivative onto the tangent space of O( n). Using this filter, an extended O( n)-constrained Kalman-like filter is developed for nonlinear systems where a portion of the states evolve on O( n). A numerical example demonstrates the effectiveness of the extended O( n)-constrained Kalman-like filter. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we study the finite-time boundedness, stabilization, and L2-gain for switched positive linear systems (SPLS) with multiple time delays. Using multiple linear copositive Lyapunov functions, sufficient conditions in terms of linear matrix inequalities are obtained for the problems of finite-time boundedness and stabilization and the design of state feedback controllers for SPLS. Under asynchronous switching, L2-gain analysis is developed for SPLS under the constraint of average dwell time. Numerical examples are given to illustrate our theoretical results. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents new results on robust positively invariant (RPI) sets for linear discrete-time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a unique scaling factor, which determines the transition from nonempty to empty RPI sets. We characterize this critical scaling factor, present an efficient algorithm for its computation, and analyze it for a number of examples from the literature. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we investigate the relationship between [ABSTRACT FROM AUTHOR]

This paper presents feedback sensitivity functions analysis of implicit Lyapunov function-based control system in case of finite-time stabilization problem. The Gang of Four is chosen as a feedback sensitivity tool. The results can be used for parametric tuning of control algorithms in order to guarantee desired closed-loop sensitivity specifications. The obtained results are supported by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Synchronization problem is investigated for multiple harmonic oscillators with identical communication delay in this paper. We propose a new distributed control algorithm in asynchronously compensated form and a corresponding reduced-order observer-based distributed control algorithm. By using frequency-domain analysis, delay-dependent and delay-independent convergence conditions are obtained for our proposed algorithms under leader-following and leaderless coordination control structures, respectively, and the results can be directly extended to the observer-based algorithm based on the separation principle. Numerical examples illustrate the validity of the theoretical findings. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of static anti-windup design for uncertain continuous-time Markovian jump systems with partially unknown transition rates in the face of actuator saturation. The underlying system is subject to time-varying and norm-bounded parameter uncertainties in both the state and input matrices. It is assumed that a set of stabilizing dynamic output-feedback controllers have been designed for the system in the absence of control saturation. The objective is to design anti-windup compensation gains for the given controllers such that the system can still be stabilized, irrespective of whether actuator saturation appears or not. To obtain a maximum estimation of the domain of attraction of the resulting closed-loop system, a convex optimization problem in the linear matrix inequality framework is formulated. Furthermore, the results are extended to the cases of the systems with completely known transition rates and with completely unknown transition rates. Finally, the usefulness of the developed method is demonstrated through simulation examples. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present the modeling and local equilibrium controllability analysis of a spherical robot. The robot consists of a spherical shell that is internally actuated by a pendulum mechanism. The rolling motion of the sphere manifests itself as a nonholonomic constraint in the modeling. We derive the dynamic model of the system using Lagrangian reduction and the variational principle. We first compute the Lagrangian and identify the symmetry with respect to a group action. The system Lagrangian and the rolling constraint are invariant with respect to the group isotropy and hence permit a reduced dynamic formulation termed as the nonholonomic 'Euler-Poincaré' equation with advected dynamics. Using Lie brackets and symmetric products of the potential and control vector fields, local configuration accessibility and local (fiber) equilibrium controllability are presented. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents a robust fault estimation approach for a class of nonlinear discrete-time systems. In particular, two sources of uncertainty are present in the considered class of systems, that is, an unknown input and an exogenous external disturbance. Thus, apart from simultaneous state and fault estimation, the objective is to decouple the effect of an unknown input while minimizing the influence of the exogenous external disturbance within the [ABSTRACT FROM AUTHOR]

Summary: This paper describes two novel schemes for fault tolerant control using robust suboptimal static output feedback design methods. These schemes can also be employed as actuator redundancy management for overactuated uncertain linear systems. In contrast to many existing methods in the literature that assume the control input matrix (i) is not of full‐rank such that it can be factorized into two matrices and (ii) it does not involve uncertainty, these schemes can be applied to systems whose control input matrix cannot be factorized and/or involve uncertainty. The so‐called virtual control, in these schemes, is calculated using suboptimal H2‐based static output feedback design schemes constructed to be robust against uncertainties emanating from inherent input matrix uncertainty and visibility of the control allocator to the controller. Then, using two proposed control allocation schemes (fixed and on‐line), the obtained virtual control signal is redistributed among remaining (redundant or nonfaulty) set of actuators. As the proposed schemes are modular‐based, they can be employed as real‐time fault tolerant control schemes with no need to reconfigure the controller in the case of actuator faults or failures. The effectiveness of the proposed schemes is discussed and compared with numerical examples. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the pth moment exponential input‐to‐state stability (ISS) of nonlinear discrete‐time impulsive stochastic delay systems. By employing Lyapunov functionals, some pth moment exponential ISS criteria are provided. The obtained results show that a discrete‐time stochastic delay system can become pth moment exponential input‐to‐state stable by impulsive controls even if it may be not input‐to‐state stable itself. On the other hand, the original system without impulses can retain its ISS property with appropriate destabilizing impulses. As an application, the theoretical results are used to test the ISS for a class of recurrent neural networks under stochastic perturbations. Finally, a numerical example is presented to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Summary: This paper concerns the consensus analysis of multiagent systems made of the interconnection of identical nonlinear agents interacting with one another through an undirected and connected graph topology. Drawing inspiration from the theory of linear "decomposable systems," we provide a method for proving the convergence (or consensus) of such multiagent sytems in the case of polynomial dynamics. The method is based on a numerical test, namely a set of linear matrix inequalities providing sufficient conditions for the convergence. We also show that the use of a generalized version of the famous Kalman‐Yakubovic‐Popov lemma allows the development of a linear matrix inequalities test whose size does not directly depend on the number of agents. The method is validated in simulation on three examples, which also show how the numerical test can be used to properly tune a controller. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the practical leader‐following consensus via the sampled‐data protocol is investigated for second‐order nonlinear multiagent systems with external disturbances, where the velocity information of all agents are assumed to be unmeasurable. The consensus problem of the multiagent system is first transformed to a stabilization problem of the constructed error system. Because of the unknown of the agents' velocities, an observer is then proposed for the constructed error system to estimate the velocity errors. By the backstepping approach, a new protocol is designed with only position measurements and sampled‐data information. Furthermore, the upper bound of the sampling period is given. It is proved that the practical leader‐following consensus can be achieved by the proposed sampled‐data protocol with a proper sampling period. The result is then extended to the multiagent systems with multiple leaders. Finally, two numerical examples are provided to illustrate the effectiveness of the designed protocols. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the problem of gain‐scheduled output feedback control design for continuous‐time linear parameter varying systems. The scheduling parameters are supposed to be measured in real time with absolute uncertainties and proportional uncertainties, simultaneously. Using a nonlinear transformation, the problem is formulated in terms of solutions to a set of parameter‐dependent linear matrix inequalities, exploiting parameter searches for two scalar values. H∞‐type problem is treated using parameter‐dependent Lyapunov and auxiliary matrices. One of the advantages of the presented method lies in its less conservatism in comparison with the available approaches. Some numerical examples are given to illustrate the effectiveness and advantage of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: In this paper, collaborative distributed dynamic output‐feedback control problem is investigated for a class of wireless control systems with Markovian‐type control network and distributed network‐induced delays. The network consists of a set of interconnected nodes characterized by a directed graph with an adjacency matrix that specifies space distribution (ie, interconnection topology). Each node of wireless control systems not only routes information but also performs its local control. We assume measurements and distributed network‐induced delays are subject to two independent Markovian chains. It is shown that the collaborative distributed dynamic output‐feedback approach offers better performances compared with noncollaborative distributed control approach. An irrigation canal system is used to demonstrate practical potentials of the developed control strategy. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the distributed tracking control of a group of underactuated quadrotors in the presence of actuator faults in three‐dimensional space. Using consensus protocol and sliding mode algorithm, a distributed finite‐time fault‐tolerant formation control scheme is developed. The whole closed‐loop system is composed by position loop, attitude loop, and propeller speed loop. A propeller speed fault‐tolerant controller is developed to deal with the unexpected faults of quadrotors. The finite‐time stability of the closed‐loop system is guaranteed through Lyapunov analysis. Finally, the efficiency of the proposed algorithm is illustrated by some numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: In this paper, an aggregative game of multiagent systems over weight‐balanced digraphs is studied, where the decisions of all players are coupled by linear constraints. Different from the well‐known aggregative games, the dynamics of players are disturbed first‐order linear systems in our problem. In order to seek the variational generalized Nash equilibrium (GNE) of the game, a distributed algorithm is developed via gradient descent, internal model, and dynamic average consensus, where the gradient is for seeking the variational GNE, the internal model is for rejecting the exogenous disturbances, and the dynamic average consensus is for estimating the aggregate of the decisions of all players. The exponential convergence of the algorithm to the variational GNE is analyzed by constructing suitable Lyapunov functions. Finally, the effectiveness of our method is illustrated via two examples. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we present the vibration control design for a string with the boundary time‐varying output constraint. The dynamics of the string is a distributed parameter system described by a partial differential equation and two ordinary differential equations. A barrier Lyapunov function with a logarithmic function is adopted to prevent the time‐varying constraint violations. Adaptive control is designed to handle the system parametric uncertainties. Stability analysis and the solvability of the inequality equations are provided. Numerical simulations are provided to illustrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

Summary: Domain of attraction plays an important role in stability analysis and safety verification of nonlinear control systems. In this paper, based on the concept of multiple Lyapunov‐like functions, we propose iteration algorithms for computing inner estimates of domains of attraction for a class of switched hybrid systems, where the state space is composed of several regions and each region is described by polyhedral sets. Starting with an initial inner estimate of domain of attraction, we firstly present a theoretical framework for obtaining a larger inner estimate by iteratively computing multiple Lyapunov‐like functions. Successively, the theoretical framework is underapproximatively realized by using S‐procedure and sums of squares programming, associated with the coordinatewise iteration method. Afterwards, for obtaining a required initial inner estimate of domain of attraction, we propose an alternative higher‐order truncation and linear semidefinite programming based method for computing a common Lyapunov function. Especially, a bisection method based improvement is proposed for obtaining better estimates in each iteration step. Finally, we implement proposed algorithms and test them on numerical examples with comparisons. These computation and comparison results show that the advantages of our multiple Lyapunov‐like functions based algorithm. Especially, we provide alternative underapproximations for avoiding the possible numerical problem. [ABSTRACT FROM AUTHOR]

Semi-Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi-Markovian systems with mode-dependent time-variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time-delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper presents LMI conditions for local, regional, and global robust asymptotic stability of rational uncertain nonlinear systems. The uncertainties are modeled as real time varying parameters with magnitude and rate of variation bounded by given polytopes and the system vector field is a rational function of the states and uncertain parameters. Sufficient LMI conditions for asymptotic stability of the origin are given through a rational Lyapunov function of the states and uncertain parameters. The case where the time derivative of the Lyapunov function is negative semidefinite is also considered and connections with the well known LaSalle's invariance conditions are established. In regional stability problems, an algorithm to maximize the estimate of the region of attraction is proposed. The algorithm consists of maximizing the estimate for a given target region of initial states. The size and shape of the target region are recursively modified in the directions where the estimate can be enlarged. The target region can be taken as a polytope (convex set) or union of polytopes (non-convex set). The estimates of the region of attraction are robust with respect to the uncertain parameters and their rate of change. The case of global and orthant stability problems are also considered. Connections with some results found in sum of squares based methods and other related methods found in the literature are established. The LMIs in this paper are obtained by using the Finsler's Lemma and the notion of annihilators. The LMIs are characterized by affine functions of the state and uncertain parameters, and they are tested at the vertices of a polytopic region. It is also shown that, with some additional conservatism, the use of the vertices can be avoided by modifying the LMIs with the S-Procedure. Several numerical examples found in the literature are used to compare the results and illustrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a distributed sensor fault detection and isolation (FDI) scheme for multimachine power systems. Each generator is interconnected with other generators through a transmission network, where the interactions between directly interconnected generators are nonlinear. In the distributed FDI scheme, a local FDI component is designed for each generator excitation system in the power system based on local measurements and certain communicated information from other FDI components associated with generators that are directly interconnected to the local generator. In each FDI component, adaptive thresholds for distributed FDI are derived, ensuring robustness with respect to nonlinear interconnection and unstructured modeling uncertainty under certain conditions. Furthermore, the fault detectability and isolability properties are investigated, characterizing the class of sensor faults that are detectable and isolable by the distributed FDI method. In addition, the stability and learning capability of the local adaptive fault isolation estimators designed for each generator is derived. A simulation example of a two-machine power system is used to illustrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a non‐iterative direct approach for controller design from experimental data; the parameters of a controller of a prescribed order and structure are optimized with respect to a relevant performance criterion. The proposed design method enjoys the following features: (i) It does not involve the identification of the process to be controlled; (ii) it only requires a single experiment; (iii) in the case of stable plants, no initial controller is needed even when the process to be controlled is non‐minimum phase; and (iv) it provides sufficient conditions for the resulting closed‐loop system to be stable. The approach builds upon the so‐called unfalsified control theory; this key point makes it possible to derive simple and intuitive relations between the choice of the performance criterion to be optimized and closed‐loop stability conditions. The analysis is supported by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: This paper presents new extended linear matrix inequality (LMI) characterizations for the synthesis of robust H ∞ and H 2 state feedback controllers for continuous‐time linear time‐invariant systems with polytopic uncertainty. Based on a suitable change of variables and the Elimination Lemma, the proposed robust control design techniques are stated as extended LMI conditions parameterized in terms of 2 scalar parameters. One parameter is shown to belong to a bounded domain, thus limiting the scalar search domain. For the other parameter, a bounded subset is provided from numerical experiments. The benefits of the methodology are illustrated through numerical simulations performed on an uncertain model borrowed from the literature. It is shown that the proposed LMI relaxations can provide less conservative results with fewer scalar searches than some existing methods in the literature. [ABSTRACT FROM AUTHOR]

This paper provides unified solutions for distributed attitude and translation consensus problems for networked fully actuated rigid bodies under the fixed and undirected communication topology with the tool of unit dual quaternion. We investigate two kinds of consensus, that is, leaderless consensus and leader-following consensus with a static leader. Firstly, the dynamics of rigid bodies are presented by unit dual quaternion. The control inputs of rigid bodies are also obtained from unit dual quaternion. Secondly, we propose a distributed consensus law in the form of dual quaternion to guarantee that the attitudes and translations of all rigid bodies reach consensus, respectively, without a leader. Thirdly, the leader-following consensus problem with a static leader is studied. With the proposed leader-following consensus law, the states of all rigid bodies converge to the corresponding states of the static leader, including the attitude and the translation. Finally, numerical examples are provided to validate the effectiveness of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a protocol and a control law are designed for a single robot so that a team of such robots can interact and cooperate to reach the displacements from an eligible reference formation. Each robot is equipped with displacement sensors of limited sensing ranges. Communication channels are assumed to be unavailable to the team, and each robot works in stealth mode. The team is scalable such that new robots can be recruited, and existing robots can be dismissed. In order for the team size to be scalable, the extended formation based on relative displacement is established as the reference formation. Thus, using the extended formation as a reference, the control law and the protocol could be flexible. As potential conflicts deflect the robot team from the desired formation, the control law is designed to expose the conflicts to the involved neighboring robots such that the protocol can resolve them. A numerical example is given to illustrate how an extended formation is designed, and a simulation example is conducted to demonstrate the performance and merits of the proposed techniques. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a novel robust sliding mode learning control scheme is developed for a class of non-minimum phase nonlinear systems with uncertain dynamics. It is shown that the proposed sliding mode learning controller, designed based on the most recent information of the stability status of the closed-loop system, is capable of adjusting the control signal to drive the sliding variable to reach the sliding surface in finite time and remain on it thereafter. The closed-loop dynamics including both observable and non-observable ones are then guaranteed to asymptotically converge to zero in the sliding mode. The developed learning control method possesses many appealing features including chattering-free characteristic, strong robustness with respect to uncertainties. More importantly, the prior information of the bounds of uncertainties is no longer required in designing the controller. Numerical examples are presented in comparison with the conventional sliding mode control and backstepping control approaches to illustrate the effectiveness of the proposed control methodology. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous-time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete-time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discrete-time domain assures a guaranteed quadratic cost to the closed-loop continuous-time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm-bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete-time domain, a digital robust state feedback control law that stabilizes the original continuous-time system assuring an upper bound to the quadratic cost of the closed-loop system. The applicability of the proposed design method is illustrated through a numerical experiment. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the robust consensus tracking problem for a class of heterogeneous second-order nonlinear multi-agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz-like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper focuses on the robust output precise tracking control problem of uncertain nonlinear systems in pure-feedback form with unknown input dead zone. By designing an extended state observer, the states unmeasurable problem in traditional feedback control is solved, and the lumped uncertainty, which is caused by system unknown functions and input dead zone, is estimated. In order to apply separation principle, finite-time extended state observer is designed to obtain system states and estimate the lumped uncertainty. Then, by introducing tracking differentiator, a modified dynamic surface control approach is developed to eliminate the 'explosion of complexity' problem and guarantee the tracking performance of system output. Because tracking differentiator is a fast precise signal filter, the closed-loop control performance is significantly improved when it is used in dynamic surface control instead of first-order filters. The L ∞ stability of the whole closed-loop system, which guarantees both the transient and steady-state performance, is shown by the Lyapunov method and initialization technique. Numerical and experiment examples are performed to illustrate our proposed control scheme with satisfactory results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of self-triggered state-feedback control for linear plants under bounded disturbances. In a self-triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on the current sampled state and on a priori knowledge about the plant. Besides comparing some existing approaches to self-triggered control available in the literature, we propose a new self-triggered control strategy that allows for the consideration of model-based controllers, a class of controllers that includes as a special case static controllers with a zero-order hold of the last state measurement. We show that our proposed control strategy renders the solutions of the closed-loop system globally uniformly ultimately bounded. We further show that there exists a minimum time interval between sampling times and provide a method for computing a lower bound for it. An illustrative example with numerical results is included in order to compare the existing strategies and the proposed one. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of solving a class of periodic discrete-time Riccati equation with an indefinite sign of its quadratic term. Such an equation is closely related to the so-called full-information H ∞ control of discrete-time periodic systems. A globally convergent iterative algorithm with a local quadratic convergence rate is proposed for this purpose. An application to the problem of H ∞ filtering of discrete-time periodic systems is also developed and illustrated via a numerical example. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper provides a deep insight into the saturated PID control of a double integrator with bounded disturbance. On the basis of the nested saturation functions, a simple PID-like controller is proposed. The main difficulty in saturation control with bounded disturbances is to prove that the unsaturated regions are invariant. By phase plane and singular perturbation analysis, we prove that the saturation restrictions on the controller can be removed one by one in finite time, and the closed-loop system can be finally reduced to a nonsaturated PID controlled double integrator. The sufficient conditions for the stability of the closed loop with disturbance are also derived. Finally, numerical simulations are conducted to validate the effectiveness of the proposed control scheme. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we consider two methods for solving differential and algebraic Lyapunov equations in the time and frequency domains. Solutions of these equations are finite and infinite Gramians. In the first approach, we use the Laplace transform to solve the equations, and we apply the expansion of the matrix resolvent of the dynamical system. The expansions are bilinear and quadratic forms of the Faddeev matrices generated by resolvents of the original matrices. The second method allows computation of an infinite Gramian of a stable system as a sum of sub-Gramians, which characterize the contribution of eigenmodes to the asymptotic variation of the total system energy over an infinite time interval. Because each sub-Gramian is associated with a particular eigenvector, the potential sources of instability can easily be localized and tracked in real time. When solutions of Lyapunov equations have low-rank structure typical of large-scale applications, sub-Gramians can be represented in low-rank factored form, which makes them convenient in the stability analysis of large systems. Our numerical tests for Kundur's four-machine two-area system confirm the suitability of using Gramians and sub-Gramians for small-signal stability analyses of electric power systems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Stability and performance features of linear PI compensation for continuous bioreactors are studied in this paper. First, it is established that conventional PI control can be represented as the combination of an I/O inverse dynamics feedback with a modeling error dynamic estimator. Then, the analysis of the closed-loop dynamics carried out with singular perturbation tools shows that PI control can recover the stability and performance induced by exact I/O inverse dynamics feedback controller. The theoretical results are illustrated via a typical numerical example. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper deals with the H∞ filtering problem for a class of discrete time-varying systems with state saturations, randomly occurring nonlinearities as well as successive packet dropouts. Two mutually independent sequences of random variables that obey the Bernoulli distribution are employed to describe the random occurrence of the nonlinearities and packet dropouts. The purpose of the addressed problem is to design a time-varying filter such that the H∞ disturbance attenuation level is guaranteed, over a given finite-horizon, for the filtering error dynamics in the presence of saturated states, randomly occurring nonlinearities, and successive packet dropouts. By introducing a free matrix with its infinity norm less than or equal to 1, the error state is bounded by a convex hull so that some sufficient conditions obtained via solving a certain set of recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when state saturations are partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed filter design approach. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stabilization problem for a class of switched affine systems with a state-dependent switching law. Since the states measurements are in general subject to perturbations and noises, we propose a robust switching-law design method. Qualitative conditions for the stability of the closed-loop switched system are given. Stability conditions are also formulated as Linear Matrix Inequalities (LMIs) to allow numerical implementations. Results are illustrated by numerical examples to show the efficiency of the method and its limits. [ABSTRACT FROM AUTHOR]

Different from both finite‐time control (where the settling time depends on the initial condition) and fixed‐time control (whose settling time is subject to an upper bound but varies due to uncertainties and nonlinearities), the prescribed‐time control achieves regulation in prescribed finite time, even under uncertain nonlinearities. This article investigates the prescribed‐time regulation problem for a class of cascaded systems with integral form and control input constraints. The establishment of prescribed‐time property consists of the prescribed‐time regulation controller and prescribed‐time explicit reference governor (PT‐ERG), both of which satisfy the prespecified time requirement. For an elegant implementation, the feasibility for the separate design of controller and governor is guaranteed through a developed prescribed‐time cascaded stable theory. For the prescribed‐time controller, the proposed smooth time‐varying controller provides the prescribed‐time convergence based on a residual‐time‐dependent scaling transformation. For the PT‐ERG dealing with the control input constraints, a reference trajectory with a fixed minimum convergence rate provides an elegant compromise between performance and constraints which keeps the constraint satisfied and tracking errors in an invariant set. Both theoretical analysis and numerical simulations verify the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]