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This paper provides a Lyapunov formulation of the cyclic-small-gain theorem for general dynamical networks (large-scale systems) composed of interconnected input-to-state stable (ISS) subsystems. ISS-Lyapunov functions for dynamical networks satisfying cyclic-small-gain are constructed from the ISS-Lyapunov functions of the subsystems.
We introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer...
The issue of the stability of linear systems with time-varying delays is considered in this paper. The time-delay considered in this paper belongs to a given interval and its derivative also belongs to a given interval. By constructing a new type of Lyapunov functional where some triple-integral terms are contained and the information of the lower bound on the delay is considered sufficiently, new...
We investigate stochastic averaging on infinite time interval for a class of continuous-time nonlinear systems with stochastic perturbation and remove several restrictions present in existing results: global Lipschitzness of the nonlinear vector field, equilibrium preservation under the stochastic perturbation, and compactness of the state space of the perturbation process. If an equilibrium of the...
Necessary and sufficient stability conditions are given for the existence of a continuous Lyapunov function for a semicontinuous, stochastic discrete-time system. The continuity of the Lyapunov function is linked to robustness of the stability property, which reduces to classical stability plus convergence for deterministic systems. The nature of the Lyapunov results are inspired by Lyapunov results...
The paper studies semi-global practical input-to-state stability (SGP-ISS) of a parameterized family of discrete-time systems that may arise when an approximate discrete-time model of a sampled-data system with disturbances is used for controller design. It is shown under appropriate conditions that if the solutions of the time varying family of discrete-time systems with disturbances converge uniformly...
We study classical families of chemostat models with an arbitrary number of species competing for a single limiting substrate. For families of models, we present some obstructions to the existence of asymptotically stabilizable periodic trajectories. For other families of growth rates, we design a dilution rate and input substrate time-varying feedback controllers so that a positive trajectory of...
This paper focuses on the analysis of some classes of observers for linear systems with a point-wise delay. First, it is pointed out that, classical interval observers for systems without delays are not robust with respect to the presence of delays that appear in a specific structure location, no matter how small it is. Next, it is shown that, in general, for linear systems classical interval observers...
This paper studies the global robust output regulation problem for a class of output feedback systems subject to an uncertain exosystem by using output feedback control. An adaptive control technique is used to handle the unknown parameter vector in the exosystem. It is shown that this unknown parameter vector can be exactly estimated asymptotically if the controller incorporates a minimal internal...
We consider arbitrarily many interconnected integral Input-to-State Stable (iISS) systems in an arbitrary interconnection topology and provide an (i)ISS comparison principle for networks. We show that global asymptotic stability of the origin (GAS) of a lower-dimensional system termed the comparison system, which is based on the individual dissipative Lyapunov iISS inequalities, together with a scaling...
Global asymptotic stabilization for a class of nonlinear systems is addressed. The dynamics of these systems are composed of a linear part to which is added some nonlinearities which satisfy two different sector bound conditions depending wether the state is closed or distant from the origin. The approach described here is based on the uniting of control Lyapunov functions as introduced in. The stabilization...
This paper presents a novel approach to design a composite adaptation law for neural networks that uses both the system tracking errors and a prediction error containing parametric information by devising an innovative swapping procedure that uses the recently developed Robust Integral of the Sign of the Error (RISE) feedback method. Semi-global asymptotic tracking is proven for an Euler-Lagrange...
We study global stabilization of strict-feedforward systems with arbitrarily long input delay. These systems may be open-loop unstable but cannot exhibit finite escape instability, providing for a possibility of global stabilization even in the presence of long delay. We derive predictor-based feedback laws for exact compensation of input delay. These feedbacks are given explicitly due to the fact...
In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in ??n. We propose a gradient based control law which achieves exponential...
A functional differential inclusion-based approach to L2-gain analysis and feedback control problems is presented for a class of discontinuous time-delay systems. Motivated by Filippov solution in the differential equations with discontinuous right-hand side, definition of the discontinuous time-delay systems forced by external signals is introduced, and a description of L2-gain property in the sense...
This study endeavors to answer the question whether stabilization is possible if only the signs of the state variables are available as feedback information. This type of feedback is encountered with relay systems and systems using quantized state values in the feedback. We found that while systems in ??2 can easily be stabilized without knowledge of the magnitude of the state variables, systems in...
This paper proposes a method to stabilize the origins of deterministic dynamical systems by state feedback control laws with Wiener processes. First, we obtain Ito-type stochastic dynamical systems by randomizing ordinary differential equation systems. Second, we design the diffusion coefficients. Then, we obtain Sontag-type global asymptotically stabilizers based on the stochastic control Lyapunov...
In this paper, we study the asymptotic stabilization of fractional-order systems using an observer-based control law. The fractional-order systems under consideration are either linear or nonlinear and affine. A generalization of Gronwall-Bellman which is proved in the appendix is used to derive the closed-loop asymptotic stability.
It is mainly discussed Lasalle's invariant principle for a class of nonlinear systems with discontinuous righthand sides on the basis of vector Lyapunov function in the framework of Filippov solutions. Assuming that the system is Lebesgue measurable and non-Lipschitz continuous, we extend Lasalle's invariant principle for a class of discontinuous dynamical systems by means of Filippov solutions and...
In this paper, the problem of feedback equivalence to a passive system is studied for a class of nonlinear stochastic systems. Based on a nonlinear stochastic KYP lemma, we investigate the relationship between a passive system and the corresponding zero-output system, which sustains a different result from the deterministic case. Following the stochastic passivity theory, a sufficient condition is...
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