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This paper deals with a new design problem of adaptive gain robust model-following/tracking controllers for a class of systems with matched and unmatched uncertainties via piecewise Lyapunov functions. In the proposed design approach, compensation inputs for matched and mismatched uncertainties for the system are introduced and the proposed adaptive gain model-following/tracking robust controller can achieve that the tracking error decreases asymptotically to zero in spite of uncertainties. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show linear matrix inequality-based sufficient conditions for the existence of the proposed controller. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The looped-functional approach has been extensively used for stability analysis of sampled-data systems. For this approach, this paper introduces two new functionals to minimise the conservatism of stability conditions. The first one is called a non-negative integral functional (NIF) that is added to the derivative of a common Lyapunov functional. The second one is a general looped-functional (GLF), whose values at sampling instants are traditionally not well-defined, and are defined here in terms of their limits. Leveraging further affine canonical Bessel-Legendre inequalities expressed by simplified polynomials, a polynomial-based NIF, a polynomial-based GLF, and a polynomial-based zero equality are tailored for obtaining hierarchical types of stability conditions in the form of linear matrix inequalities. Finally, numerical examples show that: (i) the proposed functionals lead to less conservatism when compared with several state-of-the-art methods; and, (ii) the resulting stability conditions exhibit a hierarchical characteristic in the sense that the higher level of hierarchy, the less conservatism of the criteria. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of H∞ performance analysis of 2D discrete singular stochastic system described by Roesser model which is challenging since it involves 2D random variables and the disturbance simultaneously. Sufficient conditions are established for the regularity, causality and stability of the system. The proposed results are expressed in terms of strict linear matrix inequalities. Furthermore, a mean square asymptotic stability with an $ H_{\infty } $ H ∞ disturbance level is developed. Simulation example is provided in order to illustrate the relevance of our approach. [ABSTRACT FROM AUTHOR]

We investigate the robustness, disturbance attenuation and performance capabilities of a Proportional-Integral-Retarded (PIR) controller when controlling a class of uncertain second-order systems with input disturbances. The purpose of this paper is to provide insight into the trade-offs between these conflicting requirements. This is accomplished by introducing simple delay-dependent stability conditions, expressed in linear matrix inequality form, which are used to establish the trade-offs in PIR control. In light of the obtained stability conditions, we show that improving performance comes at the cost of reduced robustness and disturbance attenuation. To our knowledge, this problem has not been addressed before and these new results provide valuable insights and systematic guidelines for designing these controllers with trade-offs in mind, thereby completing our current understanding of the tuning mechanisms in PIR control. Inspired by the application field of fuel-cell systems, experiments are carried out on a proof-of-concept switching converter prototype to demonstrate the relevance of the obtained results. [ABSTRACT FROM AUTHOR]

This paper studies the $ {H_\infty } $ H ∞ filtering problem for a class of discrete-time semi-Markov switching repeated scalar nonlinear systems with an event-triggered scheme. Considering the limitation of bandwidth, the mode-dependent event-triggered mechanism is introduced to determine whether the currently sampled sensor data is transmitted to the filter, in which the parameters of the event generator depend on the system mode. By means of a constructed time-varying Lyapunov function, the two stages of the systems jump instant and mode residence are analysed, and a linear matrix inequality technique is used to ensure the mean-square stability and $ {H_\infty } $ H ∞ performance of the filter error system. Accordingly, the co-design method of the mode-dependent time-varying filter and the event-triggered mechanism is derived for semi-Markov switching systems. Finally, a numerical simulation is given to illustrate the effectiveness and feasibility of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

A new adaptive observer is proposed for a class of uncertain time-delay parabolic systems. The uncertainties are located in both the state equation and the output equation which are also subjected to a distributed delay. Our algorithm is based on backstepping-like transformation and a classical persistent excitation condition. To illustrate the performances of this observer, simulation results are provided. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time boundedness (FTB) of linear time-invariant systems that are affected by a disturbance generated by an exosystem. By using a time-invariant quadratic Lyapunov function, Finsler's lemma and a dual system approach, new sufficient linear matrix inequalities (LMIs) conditions are given for analysis and synthesis for FTB. These results are extended: first, to finite-time stability (FTS) of linear time-invariant systems, second, to their input–output FTS associated, or not, to FTB. All the conditions are given in terms of LMIs, which make them easily tractable. Finally, the computational efficiency and the conservatism reduction of our approach are illustrated through an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, $ \mathcal {H}_{\infty } $ H ∞ observer-based consensus for a class of nonlinear multiagent systems (MASs) with actuator saturation and input delays are estimated. A new delay-dependent region partitioning approach has been introduced in multiagent systems. The state information of the leader can be obtained by designing a distributed observer for each follower. Based on the state information of the follower and the estimated state information of the neighbouring agents, a distributed controller has been developed. With the help of a novel Lyapunov–Krasovakii functional (LKF), using a region partitioning approach combined with Wirtinger inequalities, a sufficient condition is established in terms of Linear Matrix Inequality (LMI). Finally, simulation examples are presented to the applicability of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, event-triggered control for uncertain delayed neural networks (DNNs) with actuator saturation against deception attack is discussed. We propose a novel framework into which an event-triggered mechanism (ETM), actuator saturation, system uncertainty, and deception attack are combined. In the framework, the discrete ETM is employed to determine whether the sampled signal should be transmitted to controller so as to save network bandwidth, a random occurrence deception attack model satisfying Bernoulli distribution is introduced to construct the system robust, and actuator saturation is considered due to the actual complex network environment. Based on the framework, we discussed the stochastic stability of a novel delayed neural network model in a closed-loop system. By resorting to the appropriate Lyapunov–Krasovskii functional (LKF), we derive some new sufficient conditions for the stochastically stable of the system and obtain the gain of the system controller using efficient linear matrix inequality (LMI) method. Finally, a numerical example, in the end, demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This research aims to design a robust adaptive tracking controller for Chua's switched nonlinear circuit systems. The proposed adaptive composite nonlinear approach is modified in order to provide a robust controller with improved performance in the presence of uncertainties and input saturation. It is demonstrated that by employing an integral sliding mode controller that is based on a linear matrix inequality (LMI), the resultant closed-loop system can attain an exponentially boundedly stable. This technique ensures robustness to the impacts of uncertainties and input saturation and reduces the chattering phenomenon. Eventually, a simulation example of Chua's circuit system is utilised to reveal the performance and advantages of the offered approach. [ABSTRACT FROM AUTHOR]

A novel parameter-dependent anti-windup compensator is developed to improve the performance of a constrained model reference adaptive controller. The combined control structure solves the input saturation and stability problem for inertia-varying quadcopters. The control synthesis follows the conventional two-step anti-windup design paradigm where a nominal controller is designed without consideration of input saturation while the anti-windup compensator is designed to minimise deviations from nominal performance caused by saturated inputs. To account for the varying inertia of the quadcopter during package retrieval/delivery routines, inertia parameters of the vehicle/package are estimated with an online recursive identification technique. These estimates are used by the model reference adaptive controller and to schedule the parameter-dependent anti-windup compensator. Anti-windup performance and stability conditions are formulated as a set of parameter-dependent linear matrix inequalities, which when solved, yield a gain-scheduled anti-windup compensator that ensures stability and minimises deviation from nominal performance when saturation occurs. The effectiveness of the combined control scheme is demonstrated by simulations of an input-constrained quadcopter lifting a payload of unknown mass. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the boundary fixed-time stabilisation for delay reaction–diffusion systems (DRDSs). A new boundary controller is designed to achieve fixed time stability of DRDSs. Firstly, a boundary fixed-time controller is presented for DRDSs. Then based on the designed boundary controller, using Lyapunov functional method, fixed-time stability lemma and Poincaré's inequality, we obtain the criteria to guarantee the fixed-time stability of DRDSs. In addition, boundary fixed-time controller is proposed for uncertain DRDSs to reach robust fixed-time stability. Both the cases, the systems with or without uncertainties, are severally followed by a fixed time, which is an upper-bound of the settling time and irrelevant to the initial conditions. Finally, two simulation examples are given to illustrate the fixed-time stability of the controlled systems, which show the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

This study addresses the delay-dependent criteria like mean square robust exponential stability and mean square exponential stability for the uncertain neutral discrete time-varying and distributed delay differential systems under random impulsive control. By employing the random impulsive control, descriptor model transforms, and Lyapunov functional approach, we achieved the desired performance for the given system in the way of Linear matrix inequality. Finally, we justify the proposed results through numerical examples and their simulations. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of finite-time H ∞ stabilisation for neural networks (NNs) subject to mixed-type communication attacks via an improved dynamic event-triggered scheme (DETS). The complex cyber-attacks considered consist of three common types of attacks: replay attacks, deception attacks, and denial-of-service (DoS) attacks. Different from most articles which use independent Bernoulli variables to model the cyber-attacks, this paper considers these attacks into a unified Markovian jump framework for modelling. In order to save the limited network communication resources, the improved DETS is adopted. An appropriate Lyapunov–Krasovskii functional (LKF) containing the proposed improved DETS condition is constructed, and sufficient conditions are obtained to guarantee finite-time H ∞ stabilisation of the system. Then, according to a set of feasible linear matrix inequalities (LMIs), the co-design of event-trigger and H ∞ controller is given. Finally, two numerical examples are provided to demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

This paper studies the non-fragile output-feedback H ∞ control problem for event-triggered networked control system with probabilistic time-varying delay and controller gain uncertainties. With known conditional probability distribution, the time-varying delay is modelled as a Bernoulli distributed white sequences. An improved two-side closed-loop functional is constructed by using the sawtooth structure characteristic of artificial time delay. By applying the Lyapunov–Krasovskii stability theory, the lower conservative stability criterions for time-delay system are derived. Aiming at the external disturbance and the parameter uncertainty of controller gain, a non-fragile output-feedback H ∞ control strategy based on event-triggered mechanism is proposed. Moreover, a co-design scheme of controller gain and event-triggered matrix is obtained based on linear matrix inequality technique. Finally, three simulation examples are utilised to verify the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

This paper addresses novel H 2 and L 2 norm-based controller designs for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). Despite the importance of LPV/LFR systems to the control literature, there is a lack of works on this topic. The distinctive formulation of the proposed controller designs is given by using parameter-dependent Lyapunov functions in combination with slack variables and general full-block multipliers. Such proposed formulation leads to less conservative synthesis conditions characterised in terms of a finite number of linear matrix inequalities for both state-feedback and static output-feedback controllers subject to H 2 and L 2 performances for discrete-time LPV/LFR systems. Improvements obtained by the proposed controller design conditions over existing methods in the area are assessed by numerical examples. [ABSTRACT FROM AUTHOR]

This paper studies the decentralised H ∞ filtering problem for interconnected discrete-time systems. In the developed decentralised filter scheme, only local output information is available for each local filter. The dynamics of the original system and the dynamics of the proposed filter are expressed as an augmented system. The system matrices of the augmented system consist of matrix inversion terms, which are computationally expensive and even meet numerical stability problems. In order to avoid the matrix inversion computation, this paper derives novel computationally attractive sufficient conditions without inversion terms to guarantee the H ∞ performance of the augmented system. Then, these conditions are transformed into linear matrix inequalities. The decentralised filter parameters can be obtained by solving linear matrix inequalities. Finally, two simulation examples are given to demonstrate the effectiveness and the advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

This article is dedicated to the exponential stability of a class of descriptor continuous Roesser 2D linear models. One of the two dimensions is privileged so that the exponential stability must be mainly understood as the vanishing propagation of the state vector along that dimension. This stability is analysed through a tractable test based upon Linear Matrix Inequalities (LMI). [ABSTRACT FROM AUTHOR]

In this paper, the stability analysis of linear systems with time-varying delays is studied. A novel Lyapunov method is presented, in which positive definiteness of the matrices in common Lyapunov functionals is relaxed by adding what is referred to as a zero-integral functional (ZIF). A general form of auxiliary polynomial-based functionals that contains such ZIF is given. Choosing polynomials of different order as well as exploring double-delay-product (DDP) terms, novel Lyapunov functionals are constructed, which contribute to a set of improved stability conditions expressed in terms of linear matrix inequalities. Finally, numerical examples are provided to corroborate the merits of the proposed method relative to a number of existing methods, and in particular, the effectiveness of the proposed ZIFs and DDP terms in reducing the conservatism of stability conditions. [ABSTRACT FROM AUTHOR]

This paper deals with consensus in discrete-time multi-agent systems under directed networks subject to time-varying delays and input saturation. Because saturation might prevent multi-agent systems from attaining consensus, system analysis and controller design require the characterization of the allowed region for the initial conditions. The main contributions of this work are sufficient conditions for consensus analysis and design of distributed protocols for discrete-time systems. Moreover, the conditions lead to a procedure allowing an estimate of the region of attraction. Such a procedure considers the effect of current and delayed states separately, yielding broader estimates of the allowed region for initial conditions. The results follow from the transformation of the consensus problem into a stability problem, with the subsequent employment of the Lyapunov-Krasovskii theory. The conditions are formulated as convex optimization problems. Finally, the paper presents examples and comparisons with previous approaches to illustrate the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered dynamic surface controller is proposed for strict-feedback nonlinear networked systems with mismatched uncertainties. Towards this aim and first of all, an event-based dynamic surface control law is designed. Then, the closed-loop error dynamics is derived and rewritten as a linear dynamics with nonlinear perturbation terms. Next, these terms are classified into vanishing and nonvanishing perturbations. Finally, by imposing some constraints on the nonvanishing terms, an event-triggering mechanism is constructed. By formulating the imposed constraints in the form of linear matrix inequalities (LMIs) and using the ultimate boundedness theory, the ultimate error boundedness and quadratic tracking objectives are addressed in the framework of convex optimisation. The absence of the Zeno behaviour, which is an important feature of any event-triggered methodology, is also proven. The validity of the theoretical results is illustrated by applying the proposed method to a remotely operated underwater vehicle in a simulation study as well as an experimental implementation on a magnetic levitation system. [ABSTRACT FROM AUTHOR]

This paper is about the H 2 and H ∞ filtering of Markov Jump Systems subject to a class of nonlinearities which include them on the Lur'e systems framework. The proposed filters are robust to nonlinearities belonging to a given sector with maximum slope. With regard to the availability of the Markov parameter, we present strategies which allow us to design either mode-dependent and modeindependent filters, with sector bound optimisation. The results are illustrated by two examples. [ABSTRACT FROM AUTHOR]

This paper studies the global attitude stabilization of a rigid body, a task that is subjected to topological obstacles. As a result of these obstructions, continuous feedbacks cannot globally stabilise the rigid body attitude. Therefore, this paper presents an observer-based hybrid controller to overcome these restrictions. Consequently, a new kind of synergistic potential function is designed which induces a gradient vector field to globally stabilise a given set. Moreover, the gradient of the proposed potential functions is utilised to derive a hybrid observer. Furthermore, this paper considers two types of constraints: angular velocity constraint and torque constraint. Afterward, these constraints are formulated in terms of the Linear Matrix Inequalities (LMI) optimisation problem to perform constraints satisfaction. Besides, this paper introduces a novel hybrid quantiser to deal with the problem of the low-price wireless network. Finally, a comparative study in simulations is provided to assess the performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper presents the design of an observer-based quadratic boundedness protocol for leader-following consensus in multi-agent systems. The problem under consideration is to force all the agents to follow the trajectories of a virtual leader in spite of bounded disturbances which implies that the leader-following consensus is reached in a positively invariant and attractive ellipsoid. Under the framework of control synthesis in multi-agent systems subject to bounded disturbances, linear matrix inequality-based sufficient conditions are obtained for the computation of the controller and observer gains. The effectiveness of the proposed approach is demonstrated through simulations in a fleet of unmanned aerial vehicles subject to wind turbulence which are shown to achieve formation control. [ABSTRACT FROM AUTHOR]

This paper proposes an improved exponential stability analysis criterion and designs a distributed H ∞ filter for a spatially interconnected discrete-time time-varying delay (SIDTD) system. Firstly, combining the Wirtinger-based inequality with reciprocally convex combination inequality, a new and less conservative exponential stability criterion, which guarantees the well-posedness, exponential stability, and H ∞ performance of the SIDTD system, is reduced to standard linear matrix inequalities. Moreover, we design a distributed structure-preserving H ∞ filter based on the new stability result. The structure-preserving H ∞ filter and the delay-free H ∞ filter can be obtained by employing the Finsler lemma. Finally, the validity and advantages of the derived results are shown by a numerical example and a practical example. [ABSTRACT FROM AUTHOR]

The paper discusses the design of a robust fault detection system for linear discrete-time invariant uncertain systems. The intended system consists of norm-bounded uncertainty, stochastic uncertainty, and external unknown input. Due to the mixed uncertainties, H∞ based model matching technique is used to develop a robust system that offers maximum sensitivity to faults and minimum sensitivity to all other unknown inputs. Reference residual model is designed using co-inner-outer factorization and the fault detection system is designed so that the error between reference residual and robust residual generated by fault detection filter (FDF) is minimized in H∞ sense. The existing condition of FDF is exploited in terms of linear matrix inequalities. A numerical example and a benchmark three-tank system are simulated to illustrate the performance of the proposed fault detection system. Results confirm the effectiveness of the proposed approach by timely detecting the occurrence of the fault. [ABSTRACT FROM AUTHOR]

This paper investigates finite time annular domain (FTAD) stability and stabilisation for Itô-type stochastic time-varying systems with continuous Wiener and discontinuous Poisson noises (STVSWPNs). First, using Itô-Levy formula and time-varying multiple quadratic Lyapunov functions, two less conservative FTAD-stability conditions based generalised differential Lyapunov equations (GDLEs) and differential linear matrix inequalities (DLMIs) are obtained. Second, the FTAD stabilisation is studied and some new sufficient conditions for the existence of state feedback and static output feedback controllers are presented by tractable differential linear matrix inequalities. Moreover, a new numerical algorithm is given. Finally, a numerical example and a real-world example are utilised to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper presents the design of robust hierarchical control for homogeneous linear multi-agent systems (MAS) subject to parametric uncertainty and external disturbance. Specifically, the control design is based on a two-layer hierarchical structure consisting of an upper layer and a lower layer. In the lower layer, each agent is represented by a linear time-invariant system and executes a local action. Moreover, each agent exchanges information with neighbouring agents in the upper layer through an undirected graph to achieve the global goal of stabilisation and disturbance attenuation for the MAS. We propose two robust control designs, namely, robust H ∞ hierarchical control and robust H 2 hierarchical control. The design of local and global feedback control laws is formulated as a constrained optimisation over linear matrix inequalities (LMI). The LMI formulation can effectively incorporate the design objective to minimise disturbance attenuation. Numerical results show that the proposed robust controls ensure robust stability of MAS and outperform the existing nominal controls by improving the disturbance attenuation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel distributed formation controller for general linear multi-agent systems with application to multiple quadcopters. First, a new locally computable state-estimate-based event-triggering communication condition is proposed for each agent. Then, the formation tracking problem is formulated as a stability analysis, controller gain and event-generator gain design problem of the closed-loop formation error dynamics. Sufficient conditions that guarantee the co-existence of a valid formation controller and an event-triggered communication mechanism are derived using a Lyapunov-based method and linear matrix inequality techniques. In addition, equivalent low (agent-sized) dimensional sufficient conditions are obtained to reduce the computational complexity. For the simulation conditions used in this research, the proposed estimate-based event-triggered communication mechanism generates less data communication instants when compared with traditional state-error-based mechanisms while still achieving similar control performance. [ABSTRACT FROM AUTHOR]

This paper investigates exponential stability problem of integral time-varying delay system. Based on a novel exponential stability theorem, sufficient conditions for exponential stability of integral time-varying delay system are obtained in the form of coupled linear matrix inequalities (LMIs). These sufficient stability conditions cover some previous results as special cases when the integral time-varying delay system reduce to the integral time-invariant delay system. These sufficient conditions cannot be obtained directly from Theorem 1 given in Li, Zheng, and Wang [(2016). Exponential stability analysis of integral delay systems with multiple exponential kernels. Journal of the Frankline Institute, 353, 1639–1653. ] due to the presence of time-varying delays. This is the main motivation for the research being carried out in this paper. Four example s are provided to show the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of hybrid control for a class of switched uncertain systems. The switched system under consideration is subject to structured uncertain dynamics in a linear fractional transformation (LFT) form and time-varying input delays. A novel hybrid controller is proposed, which consists of three major components: the integral quadratic constraint (IQC) dynamics, the continuous dynamics, and the jump dynamics. The IQC dynamics are developed by leveraging methodologies from robust control theory and are utilised to address the effects of time-varying input delays. The continuous dynamics are structured by feeding back not only measurement outputs but also some system's internal signals. The jump dynamics enforce a jump (update/reset) at every switching time instant for the states of both IQC dynamics and continuous dynamics. Based on this, robust stability of the overall hybrid closed-loop system is established under the average dwell time framework with multiple Lyapunov functions. Moreover, the associated control synthesis conditions are fully characterised as linear matrix inequalities, which can be solved efficiently. An application example on regulation of a nonlinear switched electronic circuit system has been used to demonstrate effectiveness and usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper employs the observer-based output feedback control technique to deal with the problem of spatiotemporally asynchronous sampled-data control for a linear parabolic PDE on a hypercube. By the spatiotemporally asynchronous sampled-data observation outputs, an observer-based output feedback control law is constructed, where the sampling interval in time is bounded. By constructing an appropriate Lyapunov–Krasovskii functional candidate and applying a weighted Poincaré–Wirtinger inequality on a hypercube, it is shown under a sufficient condition presented in terms of standard linear matrix inequalities that the suggested spatiotemporally asynchronous sampled-data control law asymptotically stabilises the PDE in the spatial H 1 (Ω) norm but its convergence speed can be regulated by a known constant. Moreover, both open-loop and closed-loop well-posedness analysis are done within the framework of C 0 semi-group. Finally, numerical simulation results are presented to support the proposed design method. [ABSTRACT FROM AUTHOR]

This paper proposes a new algorithm to reduce the number of gains of a polytopic LPV controller considering generic tuples of vertices, for which a common controller gain can be used. The use of Frobenius norm and the inclusion of the input matrix in the LMIs perturbation matrix allows decreasing the conservativeness to select vertices which are combinable, with respect to a previous approach based on Gershgorin circles. A combinability metric that can be applied to an arbitrary partition of the set of vertices is defined. Then, a recursive algorithm finds a lesser-fragmented combinable partition at each iteration by combining together two elements of a partition. The algorithm aims at finding combinable partitions with minimal cardinality in fewer attempts, always preserving the original control performance specifications. The proposed method is validated using numerical examples, a twin rotor MIMO system and a two-link robotic manipulator. [ABSTRACT FROM AUTHOR]

In this paper, exponential synchronisation of nonlinear multi-agent systems with K agents by distributed self-triggered hybrid control and virtual link mechanism is investigated. Based on the Lyapunov function and linear matrix inequalities, some synchronisation conditions are provided. Because of using the virtual link, the system can be divided into two subsystems, real link subsystem and virtual link subsystem. They can be synchronised with the desired dynamical behaviours by using the same self-triggered hybrid control. Hence, the original dimension (K) of synchronisation conditions can be reduced to ⌈ K 2 ⌉ ( K 2 round up). Finally, a simulation example is given to demonstrate the performance of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper is devoted to the guaranteed cost H ∞ of continuous-time linear parameter-varying (LPV) systems, considering the gain scheduling (GS) strategy and the state derivative feedback (SDF). The main contribution of the paper is to derive linear matrix inequalities (LMIs) conditions for the H ∞ -SDF problem for LPV systems, taking into account the GS controller. For the good behaviour of the controller, we assume that the time-varying parameters are available for online measurement. In some cases, the H ∞ -GS-SDF controller obtained high control signals, and as we intend to apply the proposed method in practical situations, we introduce the concept of D -stability in the problem approach. Examples and a practical implementation show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and guaranteed cost H ∞ minimisation. [ABSTRACT FROM AUTHOR]

This paper presents some outcomes of a recently completed research project aimed at developing torque control strategies for automotive turbocharged combustion engines with modern control design methodologies. Traditional torque control consists of maintaining some relevant signals close to certain set-points generated by a map representing the static inverse model of the engine, without any consideration for the optimality of the responses. The proposed model-based control strategy does not make use of any static map and all signals of interests are regulated at the same time by a unique centralised multivariable controller. A Linear Parameter Varying (LPV) H ∞ optimal control design problem, formulated via Linear Matrix Inequality (LMI) feasibility conditions, is solved to generate the controller, whose main objectives are the reduction of fuel consumption while maintaining good torque tracking. The resulting regulator presents is gain-scheduled and is designed to be calibratable in real-time. Some numerical simulations demonstrate the effectiveness of the presented approach. [ABSTRACT FROM AUTHOR]

An interval estimation method based on the reduced-order observer and peak-to-peak analysis is proposed for continuous-time linear time-invariant systems with disturbance and measurement noise. The proposed method consists of two steps. First, a reduced-order observer with L ∞ performance is designed to obtain point estimation. Second, interval estimation is achieved by integrating the obtained point estimation and the error interval estimation by peak-to-peak analysis. Steady-state gain optimisation in terms of linear matrix inequalities is used in both steps to improve the estimation accuracy of the proposed method. The superiority of the method over the reduced-order interval observer is illustrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates a problem on event-triggered bounded consensus control for a stochastic multi-agent system with communication delay, process and measurement noises. First, according to Kalman filtering theory, the optimal state estimation of each agent is obtained and sent to its neighbour agents through the undirected network topology. Correspondingly, an event-triggered controller related to the communication delay is proposed to reduce update frequency of the controller effectively. Then, the feedback gain and triggering parameters are co-designed and solved through linear matrix inequality. Relational conclusions for bounded consensus in mean square are established for fixed and time-varying communication delays, respectively. Finally, the effectiveness of the presented results are illustrated through a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic fault and cyber-attack detection and consensus control problems are investigated for multi-agent systems. By using a Markovian approach, Linear Matrix Inequalities (LMI) are derived that incorporate relative information among the agents to detect stochastic faults and cyber-attacks and then resiliently control the system to reach a consensus. A mixed coding and Message Authentication approach is presented to detect data injection cyber-attacks on the communication links. By using the Bayesian inference, useful information regarding the cyber-attack, such as the probability of its occurrence, is derived. Simulation and two case study results corresponding to a team of multi-agent Autonomous Underwater Vehicles (UAVs) confirm and verify the effectiveness and capabilities of our proposed methodologies. [ABSTRACT FROM AUTHOR]

In this paper, the stability issue for a class of cyclic switched linear systems with all stable or partly unstable submodes is investigated. Firstly, the new concepts of stable cyclic sequence-dependent cycle dwell time (S-CDT) and unstable cyclic sequence-dependent cycle dwell time (U-CDT) are proposed for the first time. Then, based on linear matrix inequalities (multiple Lyapunov functions) and cycle dwell time (CDT) switching law, the stability conditions for slowly cyclic switched linear (nonlinear) systems with all stable submodes are established. Furthermore, by using linear matrix inequalities (multiple Lyapunov functions), S-CDT and U-CDT switching laws, the stability criteria are derived for slowly and fastly cyclic switched linear (nonlinear) systems with a designed cyclic switching scheme where slow S-CDT switching and fast U-CDT switching are, respectively, applied to partly stable and partly unstable submodes. Finally, three numerical examples are presented to demonstrate the feasibility of the developed results. [ABSTRACT FROM AUTHOR]

In this paper, the assignability of linear time-invariant (LTI) systems with respect to arbitrary control structures is addressed. It is well established that the closed-loop spectrum of an LTI system with an arbitrary control structure is confined to the set containing the fixed-modes of the system with respect to that control structure. However, the assignment of the closed-loop spectrum is not merely limited by the existence of fixed-modes in practical scenarios. The pole assignment may require excessive control effort or even become infeasible due to the presence of small perturbations in the system dynamics. To offer more insights in such more realistic scenarios, a continuous measure known as fixed-mode radius is developed. However, its evaluation is confronted with a highly non-convex optimization problem combined with the need for a combinatorial search. This study utilises properties of positive-definite cones and duality theory to formulate the assignability assessment as an optimization problem with linear matrix inequality (LMI) constraints. Based on the suggested formulation, three alternative methods are proposed to evaluate the distance to unassignability. The first two methods offer alternative non-iterative and convex programs. The third method proposes an iterative convex optimization while updating the binary variables based on the dual variables. All the proposed methods rely on convex optimization, do not involve gridding over the complex plane and circumvent the combinatorial nature of the problem by using properties of positive definite cones. Simulation results confirm the effectiveness of the proposed methods in the assessment of fixed-mode radius with respect to arbitrary control structures. [ABSTRACT FROM AUTHOR]

The problem of event-triggered control for discrete-time piecewise-affine systems subject to input saturation and bounded disturbance is investigated in this paper. An LMI-based event-triggered controller is designed to guarantee the local asymptotic stability by introducing auxiliary feedback matrices to handle input saturation. In addition, the region of attraction is well estimated. Meanwhile, by synthesising the feedback control gains and the given event-triggering condition, an optimisation problem for maximising the region of attraction is formulated in LMIs. For input-saturated piecewise-affine systems with bounded disturbance, our control objective is to reduce the influence of disturbance while reducing communication in order to guarantee that the system is uniformly ultimately bounded. The effectiveness and advantages of the proposed approaches are demonstrated by simulations. [ABSTRACT FROM AUTHOR]

This paper studies the disturbance rejection and the periodic signal tracking problems for linear systems with unknown exogenous disturbances under limited communication resources. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC). Furthermore, a periodic event-triggered feedback observer (PETFO) is proposed to reduce the computational burden and energy consumption, and saving communication resources. The PETFO observes the occurrence of a predetermined event or not, where the current data are transmitted only when the event occurs otherwise, there is a zero-order hold keeps the data unchanged. The stability of the overall systems is guaranteed using the Lyapunov Krasovskii functional theory and linear matrix inequalities (LMIs). The observer and the controller gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper focuses on the output to state description-based convergent fault tolerant control (FTC) for a class of linear time invariant (LTI) systems. An output to state description theorem is proposed, by which, an adaptive output feedback FTC with a function equation constraint is designed for the LTI system in consideration. A controller reconfiguration algorithm is proposed to solve the constraint and construct an approximate controller that can compensate effectively the fault effect on systems. Furthermore, in certain conditions, the output feedback control gains can be determined by the state feedback control gains. A linear longitudinal dynamics of an aircraft and a linearised dynamic model of a vertical takeoff and landing (VTOL) aircraft in the vertical plane are applied to illustrate the effectiveness and merits of the proposed method. [ABSTRACT FROM AUTHOR]

A novel Lyapunov-based methodology for both stability analysis and stabilisation of second-order sliding mode algorithms in the presence of exogenous disturbances is presented. Nowadays, second-order sliding modes such as the well-known super-twisting algorithm are widely recognised for their usefulness in the design of controllers, observers, and exact differentiators. However, a theoretical proof for an optimal and systematical selection of parameters for the algorithm to be stable is of particular interest. The solution proposed in this paper is based on combining exact convex representations of the nonlinear algorithms with a strict Lyapunov function, which leads to stability or design conditions in terms of linear matrix inequalities that can be efficiently solved via convex optimisation techniques, allowing us to provide an enlarged and optimal parameter setting in contrast with existing results; moreover, the systematic nature of the proposal is able to deal with different scenarios avoiding ad-hoc solutions of previous works. Effectiveness of the results is verified via simulation examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the control of systems composed of multiple coupled subsystems. In such architectures, communication between different local controllers is desired in order to achieve a better overall control performance. Any resultant improvement in control performance needs, however, to be significant enough to warrant the additional design complexity and higher energy consumption and costs associated with introducing communication channels between controllers. A practical distributed control design aims, therefore, to achieve an acceptable balance between minimising the use of communication between controllers and maximising the system-wide performance. In this article, a new approach to the problem of synthesising stabilising distributed control laws for discrete-time linear systems that balances performance and communication is presented. The approach employs a supervisory agent that, periodically albeit not necessarily at every sampling instant, solves an optimisation problem in order to synthesise a stabilising state feedback control law for the system. The online optimisation problem, which maximises sparsity of the control law while minimising an infinite-horizon performance cost, is formulated as a bilinear matrix inequality (BMI) problem; subsequently, it is then relaxed to a linear matrix inequality (LMI) problem, and (i) convergence to a solution as well as (ii) that early termination guarantees a feasible (but suboptimal) control law are proved. Stability of the closed-loop system under what is a switched control law is guaranteed by the inclusion of dwell-time constraints in the LMI problem. Finally, the efficacy of the approach is demonstrated through numerical simulation examples. [ABSTRACT FROM AUTHOR]

We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterise the feasibility of this problem using a linear matrix inequality. In particular, conditions for existence and uniqueness of optimal controls are derived, which are weaker compared to the standard approaches in the literature. We further show that also for the stochastic problem, the optimal control is given in terms of the stabilising solution of the Lur'e equation, which generalises the algebraic Riccati equation. We conclude our paper by examining an application of our theory to fluid dynamics problems. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of observer-based control for cyber-physical systems (CPSs) with incomplete measurements. The CPSs are described as a class of nonlinear strict-feedback systems. When data transmission problems, such as information packet losing or transmission medium saturation, occur, the state variables become unavailable or distorted. To solve these problems, two-state estimators are constructed for different transmission cases, based on which two backstepping controllers are designed. The stability conditions of the state estimators and closed-loop system are derived by solving a linear matrix inequality (LMI). It is proved that the control methods can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded (UUB) in mean square. The effectiveness of the proposed methods is confirmed by a simulation example. [ABSTRACT FROM AUTHOR]

This paper presents an observer-based decentralized H ∞ output feedback preview tracking control method for a class of nonlinear disturbed interconnected discrete systems. The considered output tracking control problem, for the first time, is transformed into a H ∞ controller design problem of N augmented error subsystems. For each subsystem, the suggested control law is formulated by a combination of integral control action, observer-based state feedback control action and preview feedforward action of this subsystem. Based on the Lyapunov function approach, the auxiliary matrix variable approach, and some special mathematical manipulations, the controller feasibility conditions are established in linear matrix inequality (LMI) framework to guarantee the existence of the offered observer-based decentralized H ∞ preview tracking controller. And, the gain matrices of both decentralized observation and decentralized tracking control can be searched concurrently by only one-step LMI procedure. Finally, two examples are presented to verify the effectiveness and superiority of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, the problem of state estimation for a class of uncertain, and possibly unbounded, nonlinear systems is tackled. In order to deal with such a problem, a nonlinear observer is proposed based on a continuous homogeneous and Levant's nth order differentiators. The proposed nonlinear observer provides finite-time convergence and the observer synthesis is formulated in terms of some linear matrix inequalities (LMIs). Moreover, contrary to what the literature shows, the finite-time observer does not require any type of Bounded-Input Bounded-State (BIBS) condition. Some simulation results illustrate the effectiveness of the proposed finite-time observer applied to an unstable nonlinear system. [ABSTRACT FROM AUTHOR]