Search

In this article, a descriptor method is introduced for designing static output-feedback controllers for linear, continuous-time, retarded, stochastic systems that achieves a prescribed $H_{\infty } {\kern2.84526pt}$ performance. A design solution is obtained for the uncertain case, where the parameters of the system matrices reside in a given polytope. The latter solution enables the derivation of the required constant output gain by solving a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope. The theory developed is also extended to the gain-scheduling case, and it is demonstrated by two examples. The first example compares various solution methods and the second is one of robust pitch control of an aircraft. [ABSTRACT FROM AUTHOR]

Various efforts have been devoted to developing stabilizing distributed model predictive control (MPC) schemes for tracking piecewise constant references. In these schemes, terminal sets are usually computed offline and used in the MPC online phase to guarantee recursive feasibility and asymptotic stability. Maximal invariant terminal sets do not necessarily respect the distributed structure of the network, hindering the distributed implementation of the controller. On the other hand, ellipsoidal terminal sets respect the distributed structure, but may lead to conservative schemes. In this article, a novel distributed MPC scheme is proposed for reference tracking of networked dynamical systems, where the terminal ingredients are reconfigured online depending on the closed-loop states to alleviate the aforementioned issues. The resulting nonconvex infinite-dimensional problem is approximated using a quadratic program. The proposed scheme is tested in simulation, where the proposed MPC problem is solved using distributed optimization. [ABSTRACT FROM AUTHOR]

This article presents conditions to assure the mean-square stability of linear parameter-varying systems with Markov jumps. The model dynamics are driven not only by a Markov chain but also by time-varying parameters that take values in a polytopic set. No assumption is imposed on how the parameters vary within the polytopic set, i.e., the variation rate can be arbitrarily fast. The proposed conditions stem from a homogeneous polynomial Lyapunov function in the state space, adapted to account for Markov jumps. The stability certificate is sought through linear matrix inequalities. Numerical examples illustrate this article’s contribution. [ABSTRACT FROM AUTHOR]

In this article, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant input-vector fields and linear output functions. First, we study incremental properties in the GD balancing framework. Next, based on these analyses, we provide GD linear quadratic Gaussian (LQG) balancing and GD $H_\infty$ -balancing as controller reduction methods for nonlinear systems by focusing on linear feedback and observer gains. Especially for GD $H_\infty$ -balancing, we clarify when the closed-loop system consisting of the full-order system and a reduced-order controller is exponentially stable. All provided methods for controller reduction can be relaxed to linear matrix inequalities (LMIs). [ABSTRACT FROM AUTHOR]

A simple, necessary, and sufficient condition ensuring that a real matrix of dimension three is similar to a Metzler matrix is exhibited. When this condition is satisfied, a construction of the transfer matrix is given. This construction is used to design an interval observer for a family of continuous-time systems. An example is provided with interval observer design for the so-called love dynamics in the case of limit cycles [ABSTRACT FROM AUTHOR]

The goal of this article is to investigate new and simple convergence analysis of dynamic programming for the linear–quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of both matrix inequalities and matrix norm. Under a mild assumption on the initial parameter, we prove that the $Q$ -value iteration exponentially converges to the optimal solution. Moreover, a global asymptotic convergence is also presented. These results are then extended to the policy iteration. We prove that in contrast to the $Q$ -value iteration, the policy iteration always converges exponentially fast. An example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this article, we study a class of generalized Persidskii systems with external disturbances and establish conditions, in the form of linear matrix inequalities, for input-to-output stability and robust synchronization for these systems. We apply the obtained results to the robust control design for synchronizing linear systems and to the synchronization of Hindmarsh–Rose models of neurons. [ABSTRACT FROM AUTHOR]

In this article, we study decentralized nonconvex finite-sum minimization problems described over a network of nodes, where each node possesses a local batch of data samples. In this context, we analyze a single-timescale randomized incremental gradient method, called GT-SAGA. GT-SAGA is computationally efficient as it evaluates one component gradient per node per iteration and achieves provably fast and robust performance by leveraging node-level variance reduction and network-level gradient tracking. For general smooth nonconvex problems, we show the almost sure and mean-squared convergence of GT-SAGA to a first-order stationary point and further describe regimes of practical significance, where it outperforms the existing approaches and achieves a network topology-independent iteration complexity, respectively. When the global function satisfies the Polyak–Łojaciewisz condition, we show that GT-SAGA exhibits linear convergence to an optimal solution in expectation and describe regimes of practical interest where the performance is network topology independent and improves upon the existing methods. Numerical experiments are included to highlight the main convergence aspects of GT-SAGA in nonconvex settings. [ABSTRACT FROM AUTHOR]

In robust control under state constraints, the set of admissible inputs is usually considered as given, under the assumption that the actuators have been already designed. However, if the input set is too small, any controller will fail in stabilizing the closed-loop system while satisfying all prescribed constraints for some initial states of interest, or vice versa the chosen actuators may be oversized. To handle this issue, in this article, we address the problem of computing the smallest input constraint set such that the closed-loop system is stabilizable from a prescribed set of initial states while respecting all constraints. We focus our attention on linear systems with additive disturbances, and develop the algorithm based on recursive feasibility of robust model predictive control. We demonstrate the results using numerical examples, in which we consider different metrics for the input constraint set selection. [ABSTRACT FROM AUTHOR]

Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this article is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and $H^\infty$ disturbance attenuation performance. This article first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault-tolerant $H^\infty$ control problem to the dissipation properties and the solutions of Riccati differential equations, an $H^\infty$ controller for the quantum system is then designed by solving a set of linear matrix inequalities. In particular, an algorithm is employed to introduce additional quantum inputs and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. Also, we propose a real application of the developed fault-tolerant control strategy to quantum optical systems. A linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values due to the fault processes, can be modeled as a linear Markovian jumping system. It is demonstrated that a quantum $H^\infty$ controller can be designed and implemented using some basic optical components to achieve the desired control goal for this class of systems. [ABSTRACT FROM AUTHOR]

In Niu and Ho (2014), an interesting issue was investigated on how an existing controller can still achieve the same control performance under the quantization case by designing the online adjusting strategy for the quantizer’s parameter. However, the above-mentioned work ignored the limitation of the coding length in the practical transmitting procedure such that the desirable performance may not be achieved due to the inevitable coding errors. Hence, this article will further consider the above-mentioned issue under the limited coding length. Different coding rules are designed for the quantized states and the adaptive quantizer’s parameters. The minimum bound of coding errors is explicitly given, which are dependent on the coding length and the coding range. Moreover, the relation between the coding length and the control performance is established, that is, the coding length has a direct effect on the convergent upper bound of the system state and the sliding domain around the specified sliding surface. Finally, an operational amplifier circuit system is provided to verify the proposed method. [ABSTRACT FROM AUTHOR]

This article investigates the multiplayer pursuit-evasion (MPE) differential games in the presence of malicious pursuers. First, three types of malicious pursuers, namely greedy, lazy, and traitorous pursuers are formulated by using two subjectively malicious factors in the performance index. Then, an N-player nonzero-sum game framework is established to study the relationships among healthy pursuers, malicious pursuers, and evaders. The capturability and Nash equilibrium of such a new MPE differential game are rigorously analyzed. Finally, the effects of malicious pursuers on the capture time are explicitly quantified by the minimal pursuit coefficient, whose explicit form is obtained by the solutions from coupled Riccati differential equations. [ABSTRACT FROM AUTHOR]

Considering a discrete-time linear parameter-varying systems with input constraints, this article deals with the codesign of a parameter-dependent state-feedback controller and a new parameter-dependent event-triggering mechanism. Two independent event-triggering policies are introduced at the sensor node to economize the limited network resources. They indicate whether the current state or the current scheduling parameters should be transmitted to the controller or not. In this sense, the controller scheduling parameters can differ from those of the system, yielding a certain degree of robustness concerning parameter deviations. Sufficient conditions, given in terms of linear matrix inequalities, ensure the regional asymptotic stability of the closed loop. To formulated them, we use the Lyapunov theory along with the generalized sector condition. Moreover, we formulate a convex optimization procedure indirectly reducing the transmission activity over the network. The proposed methodology effectiveness is attested through numerical examples and comparisons with related works from the literature. [ABSTRACT FROM AUTHOR]

This article deals with the input–output finite-time stability (IO-FTS) of linear discrete-time systems. In current control science, discrete-time systems play a very important role in many engineering contexts. Moreover, many discrete-time control problems are defined over a finite-interval of time; therefore, the development and application of finite-time control methodologies is of particular relevance. The first contribution of this article is a pair of necessary and sufficient conditions for IO-FTS. The former involves the solution of a set of generalized difference Lyapunov equations; the latter allows one to establish the feasibility of an optimization problem by solving a set of difference linear matrix inequalities (DLMIs). The second contribution of this article is a theorem for IO finite-time stabilization via state feedback, followed by a more general one for stabilization via output feedback. Both conditions are necessary and sufficient, and lead to optimization problems cast in the form of DLMIs. The applicability of the devised results is illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

This work is concerned with a compositional technique for the construction of finite abstractions (a.k.a., finite Markov decision processes (MDPs)) for networks of discrete-time stochastic switched systems. We propose a framework based on a notion of stochastic simulation functions, using which one can quantify the probabilistic distance between original interconnected stochastic switched systems and their finite MDPs by leveraging dissipativity-type compositional conditions. We show that the proposed compositionality conditions can enjoy the structure of the interconnection topology and be potentially fulfilled independently of the number or gains of subsystems. We also propose an approach to construct finite MDPs together with their corresponding stochastic simulation functions for nonlinear stochastic switched systems satisfying some incremental passivity property. We show that for a particular class of nonlinear stochastic switched systems whose nonlinearities satisfy an incremental quadratic inequality, the aforementioned property can be readily checked by some linear matrix inequalities. To demonstrate the effectiveness of the proposed results, we apply our approaches to the following two different case studies: a road traffic network, and a fully interconnected network of nonlinear switched systems accepting different dissipativity properties. [ABSTRACT FROM AUTHOR]

In a recent article, we have shown how to learn controllers for unknown linear systems using finite-length noisy data by solving linear matrix inequalities. In this article, we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system. [ABSTRACT FROM AUTHOR]

This technical article investigates the problem of event-triggered gain-scheduling control of nonlinear systems. The considered class of nonlinear systems is such that an equivalent local polytopic model is obtained. By following the codesign approach, it is performed the simultaneous design of the dynamic event-triggering mechanism (ETM) and the gain-scheduled controller parameterized in terms of state-dependent scheduling functions. As the state information is only available to the controller at specific instants determined by the ETM, the scheduling functions of controller and plant polytopic model are asynchronous. To cope with this drawback, the trigger function of the dynamic ETM is appropriately defined to mitigate the influence of asynchronous scheduling functions in the Lyapunov stability-based analysis, allowing to derive a less conservative codesign condition. A convex optimization problem with linear matrix inequality constraints is proposed to perform the codesign and to enlarge the interevent times. Also, it is shown that there exists a lower bound for the interevent times, which prevents Zeno behavior. Numerical examples are provided to illustrate the advantages of the proposed dynamic event-triggered control codesign approach over emulation-based approach and its static counterpart. [ABSTRACT FROM AUTHOR]

This technical note investigates the positive consensus problem of multiagent systems with directed communication topologies, where all the agents have identical continuous-time positive linear dynamics. Existing works of such a problem mainly focus on the case, where networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In contrast to them, we study this problem in which the communication topologies of the multiagent system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Based on the existing results in spectral graph theory and positive linear systems theory, several necessary, and sufficient conditions on positive consensus of the directed multiagent system are derived through using linear matrix inequality techniques. A primal-dual iterative algorithm is developed for the computation of solutions. Finally, several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel class of piecewise smooth Lyapunov functions leading to linear-matrix-inequality-based stability/performance analysis and control design for linear systems with saturating inputs. We provide conditions for global properties, and also conditions for local properties and guaranteed estimates of the basin of attraction. The backbone of our result consists in using quadratic forms with constant matrices that are not necessarily sign definite, thereby providing additional degrees of freedom. Using generalized sector conditions involving the dead-zone nonlinearity and its derivative, we formulate convex optimization conditions to verify their positivity in the region of interest. Several numerical examples with connections to existing results illustrate the potential behind our novel construction. [ABSTRACT FROM AUTHOR]

Semilinear discrete-time control systems with periodic coefficients are considered. The problem of uniform global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has a Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic semilinear discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Moreover, the converse Lyapunov theorem on Lyapunov (nonasymptotic) stability is proved for complex and real linear periodic discrete-time systems. Finally, examples of using the obtained results are presented. [ABSTRACT FROM AUTHOR]

The Lyapunov equation for polytopic linear inclusions over the space of Minkowski functions of nonempty compact and convex sets that contain the origin as an interior point is studied. In particular, necessary and sufficient conditions for the characterization, existence, and uniqueness of its fundamental solution are derived. [ABSTRACT FROM AUTHOR]

A novel sliding mode control design method is developed to address the robust stabilization problem for uncertain time-varying networked control systems subject to state delay, which utilizes auxiliary matrices to avoid the difficulties of finding quadratic Lyapunov functions and solving the linear matrix inequalities. By embedding the original system into a higher dimensional system, simplified piecewise nonnegative functions can be used to analyze the system. Stability criteria are obtained which can be satisfied and verified easily. An optimization problem is defined based on these criteria, to obtain the sliding mode control parameters to ensure the exponential stability of the closed-loop system. [ABSTRACT FROM AUTHOR]

This article presents strategies for state-feedback control law design of nonlinear control laws with saturating inputs. The input constraints are handled by considering a generalized local sector inequality allowing the study of nonsymmetric saturation bounds. A numerical formulation is presented for polynomial systems and is based on the solution of Lyapunov inequalities with sum-of-squares programming. [ABSTRACT FROM AUTHOR]

In this article, we present a convex optimization framework to verify the reachability of a desired set for discrete-time linear time-invariant systems. Given elliptically bounded inputs, the set of reachable states in $N$ time steps is the Minkowski sum of a finite number of ellipsoids. We formulate the inclusion verification problem as a chain of constraints in the form of linear matrix inequalities. As the time horizon grows, the number of constraints becomes unwieldy, and we present a technique to achieve a similar level of accuracy with far fewer terms, significantly reducing the computational cost of the method. Numerical examples presented in this article show that the method is highly adaptable. [ABSTRACT FROM AUTHOR]

In this article, the local stabilization problem is dealt with for a class of continuous-time multiple input-delay systems subject to saturating actuators. Using the generalized sector conditions and the piecewise Lyapunov–Krasovskii functional, and carrying out rigorous mathematical deduction, a sufficient condition is established under which the closed-loop dynamics is exponentially stable for admissible initial conditions. Subsequently, the explicit characterization of controller gains is obtained in terms of the solvability of linear matrix inequalities. The special cases concerning the constant and single delays are also discussed. Moreover, optimization problems are proposed to maximize the estimate of the domain of attraction. Finally, two examples are given to show the effectiveness and advantages of the obtained results. [ABSTRACT FROM AUTHOR]

The purpose of this article is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution, while the regularizers are assumed deterministic, but are not required to be differentiable or even continuous. The individual, regularized, cost functions are distributed across a strongly connected network of agents, and the Pareto optimal solution is sought by appealing to a multiagent diffusion strategy. To this end, the regularizers are smoothed by means of infimal convolution, and it is shown that the Pareto solution of the approximate smooth problem can be made arbitrarily close to the solution of the original nonsmooth problem. Performance bounds are established under conditions that are weaker than assumed before in the literature and, hence, applicable to a broader class of adaptation and learning problems. [ABSTRACT FROM AUTHOR]

This article focuses on model predictive control (MPC) design in the context of sampled-data control systems with full-state measurements. It is shown that recent results on this area can be successfully generalized to cope with sampled-data MPC. The open-loop plant is subjected to polytopic parameter uncertainty and at sampling times, a controlled output variable satisfies a set of convex constraints. A guaranteed ${\mathcal H}_2$ performance index with infinity horizon is minimized such that the feedback control preserves asymptotic stability and feasibility. The design conditions are expressed through differential linear matrix inequalities. Continuous-time systems are treated with no kind of discrete-time modeling approximation. Comparisons with classical methods from the literature dealing with continuous-time systems are presented and discussed. Examples are included for illustration. [ABSTRACT FROM AUTHOR]

In this article, for Itô stochastic systems with aperiodic sampling and multiple time-delays, we provide two different types of mean square exponential stability analysis methods. One method is based on the Razumikhin-type theorems method, based on this method, the mean square exponential stability criteria of the system are proposed. Meanwhile, mean square exponential practical stability criteria are also proposed. In addition, through these theorems, the constraint of positivity on the Lyapunov function for all times can be relaxed to sampling times for Itô stochastic systems with aperiodic sampling and multiple time-delays is proved. Another method is based on the looped-functionals method. Two looped-functionals are introduced to analyze the stability of Itô stochastic systems with aperiodic sampling and multiple time-delays. One functional is one-sided, while the other functional is two-sided. Based on these two functionals and the Itô formula, two mean square exponential stability criteria are presented in the form of linear matrix inequalities. Numerical examples are used to illustrate that the proposed approach is less conservative than other methods. [ABSTRACT FROM AUTHOR]

Using the notion of exponential QSR-dissipativity (i.e., dissipativity with respect to a quadratic supply rate given in terms of real matrices Q, S,R), this article presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article addresses the problem of sliding-mode control (SMC) of linear uncertain systems with impulse effects. The difficulty in solving such problem lies in that the continuity property of the well-used linear sliding function is lost under the intermittent impulsive action. In order to overcome this difficulty, a piecewise linear sliding function considering the dynamics properties of impulses is introduced, which turns out to be continuous along the trajectories of the impulsive system. Then, a suitable integral SMC law with switching feedback gains is constructed to guarantee the reachability of the designed sliding surface in a finite time. The resulting sliding-mode dynamics is modeled by an impulsive switched system whose stability is analyzed by applying a piecewise discontinuous Lyapunov function. Next, a sufficient condition for the existence of integral SMC law is derived in terms of linear matrix inequalities. Finally, a numerical example with several different types of impulses is provided to validate the theoretical results, which shows that the switching gain-based design contributes to the robustness of the sliding-mode controller. [ABSTRACT FROM AUTHOR]

This article deals with the stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys prespecified restrictions on switches between the subsystems and dwell times on the subsystems. We derive sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set of purely time-dependent switching signals that obeys the given restrictions. The main apparatuses for our analysis are (matrix) commutation relations between certain products of the subsystems matrices and graph-theoretic arguments. [ABSTRACT FROM AUTHOR]

In this article, a robust nonlinear model reference adaptive control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of linear matrix inequalities. Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than that provided by a classic MRAC. [ABSTRACT FROM AUTHOR]

This article is concerned with robust stability analysis of feedback interconnections of nonlinear systems using integral quadratic constraints (IQCs). Its main purpose involves reconciling hard (a.k.a. unconditional) IQC and soft (a.k.a. conditional) IQC-based analysis. In particular, it is shown that the hard IQC stability result can be recovered from the soft IQC theory. The hard IQC approach is closely related to the dissipativity theory, whereas the soft IQC approach makes use of homotopies that are continuous in the gap distance measure. [ABSTRACT FROM AUTHOR]

In this article, a decentralized adaptive sliding mode control scheme is proposed for stabilization of large-scale semi-Markovian jump interconnected systems, in which dead-zone linearity in the input and unknown interconnections among subsystems are tackled. First, by designing an integral sliding surface for each subsystem, local sliding mode dynamics are obtained in good property of dynamics. Second, sufficient conditions are established for checking the stochastic stability of the sliding mode dynamics with generally uncertain and unknown transition rates. Third, a variable structure controller is designed to guarantee finite-time reachability of sliding surface, and the unknown interconnections among subsystems are compensated by adaptive laws. Finally, a numerical example is provided to verify the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This article addresses sampled-data control of 2-D Kuramoto–Sivashinsky equation over a rectangular domain $\Omega$. We suggest to divide the 2-D rectangular $\Omega$ into $N$ subdomains, where sensors provide spatially averaged or point state measurements to be transmitted through communication network to the controller. Note that, differently from 2-D heat equation, here, we manage with sampled-data control under point measurements. We design a regionally stabilizing sampled-data controller applied through distributed in space characteristic functions. Sufficient conditions ensuring regional stability of the closed-loop system are established in terms of linear matrix inequalities (LMIs). By solving these LMIs, we find an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example demonstrates the efficiency of the results. [ABSTRACT FROM AUTHOR]

This article investigates the problem of designing $\mathcal {H}_{2}$ robust (or gain-scheduled) static output-feedback (or state-feedback) controllers for discrete-time positive linear systems affected by time-invariant (or time-varying) parameters belonging to a polytope. For this purpose, an iterative procedure based on robust (parameter-dependent) linear matrix inequalities (LMI) is proposed. Unlike most approaches, where the controller is obtained by means of a change of variables, the synthesis conditions deal with the control gain directly as an optimization variable, which is specially appealing to cope with closed-loop positivity or structural constraints. The existence of feasible initial conditions for the iterative procedure and some relaxation strategies adopted to reduce the conservativeness of the method are also discussed. Numerical examples borrowed from the literature and statistical comparisons show that the proposed technique is in general less conservative than other approaches, providing solutions and handling cases where traditional design techniques for positive systems cannot be applied. [ABSTRACT FROM AUTHOR]

A novel Lyapunov methodology for the stability check of nonlinear discrete-time switching systems, equipped with switches digraphs and nonuniform dwell-time ranges, is here presented. The novelty of the methodology consists in the following coexisting features: i) the global uniform (with respect to compact sets of initial conditions and switching signals) asymptotic stability is addressed; ii) the information on allowed switches and (nonuniform) dwell-time ranges is fully exploited; iii) no assumption is introduced on either stability or instability of the subsystems; iv) no assumption is introduced on the regularity of the functions describing the dynamics; v) the number of involved Lyapunov functions is always equal to the number of different modes; vi) a set of Lyapunov inequalities is uniquely defined coping with all scenarios of allowed switches and dwell-time ranges; vii) the provided Lyapunov conditions are necessary and sufficient for the global uniform asymptotic stability. Linear matrix inequalities obtained by this methodology are shown for the linear case. [ABSTRACT FROM AUTHOR]

For a class of generalized Persidskii systems, whose dynamics are described by superposition of a linear part with multiple sector nonlinearities and exogenous perturbations, the conditions of practical stability, instability, and oscillatory behavior in the sense of Yakubovich are established. For this purpose, the conditions of local instability at the origin and global boundedness of solutions (practical input-to-state stability) are developed in the form of linear matrix inequalities. The proposed theory is applied to investigate robustness to unmodeled dynamics of nonlinear feedback controls in linear systems, and to determine the presence of oscillations in the models of neurons. [ABSTRACT FROM AUTHOR]

This article addresses the problems of establishing structural stability and the $\mathcal {L}_2$ gain of 2-D mixed continuous–discrete time systems. The first contribution is to show that Lyapunov functions quadratically dependent on the frequency are exact for establishing structural stability. This is particularly important since the existing works that exploit Lyapunov functions provide a much larger upper bound on the dependence on the frequency or other parameters. The second contribution is to propose a novel linear matrix inequality (LMI) necessary and sufficient condition for establishing the existence of such Lyapunov functions. It is shown, analytically and through several examples, for both best and worst cases, that the numerical complexity of this novel condition is significantly smaller than that of the existing methods. The third contribution is to show that the proposed methodology can be used to establish upper bounds on the $\mathcal {L}_2$ gain, in particular, deriving a novel necessary and sufficient LMI condition based on Lyapunov functions quadratically dependent on the frequency. Finally, the article presents the generalization of the proposed methodology to nonmixed 2-D systems. [ABSTRACT FROM AUTHOR]

We provide two extensions of Halanay’s inequality, where the scalar function in the usual Halanay’s inequality is replaced by a vector valued function, under a Metzler condition. We provide an easily checked necessary and sufficient condition for asymptotic convergence of the function to the zero vector in the time-invariant case. For the time-varying cases, we provide a sufficient condition for this convergence, which can be easily checked when the systems are periodic. We illustrate our results in cases that are beyond the scope of prior asymptotic stability results. [ABSTRACT FROM AUTHOR]

This article provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for systems with general stochastic dynamics, and associated Lyapunov inequalities are derived. The system dynamics may depend on any type of stochastic process in our framework. Our results for the unified framework can immediately lead us to more specific and tractable stability conditions when the underlying stochastic process is restricted to a more definite one. Usefulness of the developed framework is demonstrated through three selected applications. [ABSTRACT FROM AUTHOR]

This article considers the design of optimal static output feedback controllers with priori structural constraints for linear systems. The structural constraints impose individual elements of the feedback matrix to satisfy certain equality or inequality constraints. The barrier method is used to address an auxiliary minimization problem to attain an approximate solution to the original nonconvex constrained optimization problem. The Lagrange multiplier method is applied to derive necessary conditions for the optimal solution. An easy-to-implement algorithm based on the gradient descent method is developed to solve the auxiliary minimization problem, and the convergence of the algorithm is proven. The effectiveness of the proposed methodology is validated using two numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we study the digital implementation of derivative-dependent control for consensus of stochastic multiagent systems. The consensus controllers that depend on the output and its derivatives are approximated as delayed sampled-data controllers. First, we consider the $n$ th-order stochastic multiagent systems. Second, we consider PID control of the second-order stochastic multiagent systems. For the consensus analysis, we propose novel Lyapunov functionals to derive linear matrix inequalities that allow us to find an admissible sampling period. The efficiency of the presented approach is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this article. We provide both strict and nonstrict versions of this S-lemma, which are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive nonconservative design methods for quadratic stabilization, $\mathcal {H}_2$ and $\mathcal {H}_{\infty }$ control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach, thus, enables control design from large datasets. [ABSTRACT FROM AUTHOR]

In the present article, we consider network-based control of linear systems with state multiplicative noise. For the sensor-controller network, round-robin, try-once-discard, and independent and identically distributed protocols are proposed to orchestrate the measurement transmission from multiple sensor nodes. By using the time-delay approach to networked control systems, sufficient conditions for the exponential mean-square stability are obtained in terms of linear matrix inequalities. Moreover, a discrete-time dynamic event-trigger is suggested to reduce the number of sent control signals from controller to actuator. An air vehicle system from the literature illustrates the efficiency of the presented approach. [ABSTRACT FROM AUTHOR]

We present a switching observer for a class of nonuniformly observable systems that are affine in the unmeasured states and nonlinear in the measured output. Using a singular time-rescaling, the dynamics of the estimation error is transformed into that of a bimodal switched linear system. Sufficient conditions that guarantee the observer’s uniform asymptotic stability are provided; these are stated in terms of persistency of excitation and dwell-time of the (output-dependent) time-scaling function evaluated along the trajectories of the system. Unlike most results on switching observers, our approach does not rely on the solution of a set of linear matrix inequalities to compute the observer gain. In addition, we compare our scheme against the Kalman observer in a particular, but meaningful, case-study of observer-based control in automotive systems. [ABSTRACT FROM AUTHOR]

A state observer and unknown input and output disturbance estimators are proposed for discrete-time linear systems corrupted by bounded unknown inputs and output disturbances. Necessary and sufficient conditions for the existence of the state observer and disturbance estimators are given. Relationships with the strong observer of Hautus are investigated. The state, unknown input, and output disturbance estimation errors are guaranteed to be $\ell _{\infty }$ -stable with prescribed performance level. The design of the state observer and disturbance estimators are given in terms of linear matrix inequalities. The proposed estimators can be applied to detect adversarial attacks on the communication channels between the controller and actuators and between the plant sensors and the controller. [ABSTRACT FROM AUTHOR]

We propose an impulsive stabilization method for delay equations based on a reduction to the center-unstable manifold. Our approach does not make use of the constructions of Lyapunov’s direct method, such as Lyapunov functions or functionals. Necessary and sufficient conditions for when a system can be stabilized by impulses are derived based on these ideas, which subsequently lead to impulsive stabilization heuristics that are amenable to implementation in a scientific computing environment. Two examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]