616 research outputs found

    Transverse Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle

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    This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI), thus allowing convex optimization tools such as sum-of-squares programming to be used to search for certificates of the existence of a stable limit cycle. Many desirable properties of contracting dynamics are extended to this context, including preservation of contraction under a broad class of interconnections. In addition, by introducing the concepts of differential dissipativity and transverse differential dissipativity, contraction and transverse contraction can be established for large scale systems via LMI conditions on component subsystems.Comment: 6 pages, 1 figure. Conference submissio

    Variance-constrained dissipative observer-based control for a class of nonlinear stochastic systems with degraded measurements

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    The official published version of the article can be obtained from the link below.This paper is concerned with the variance-constrained dissipative control problem for a class of stochastic nonlinear systems with multiple degraded measurements, where the degraded probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over a given interval. The purpose of the problem is to design an observer-based controller such that, for all possible degraded measurements, the closed-loop system is exponentially mean-square stable and strictly dissipative, while the individual steady-state variance is not more than the pre-specified upper bound constraints. A general framework is established so that the required exponential mean-square stability, dissipativity as well as the variance constraints can be easily enforced. A sufficient condition is given for the solvability of the addressed multiobjective control problem, and the desired observer and controller gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programming method. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed algorithm.This work was supported in part by the Distinguished Visiting Fellowship of the Royal Academy of Engineering of the UK, the Royal Society of the UK, the GRF HKU 7137/09E, the National Natural Science Foundation of China under Grant 61028008, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany

    Well-posedness and Stability for Interconnection Structures of Port-Hamiltonian Type

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    We consider networks of infinite-dimensional port-Hamiltonian systems Si\mathfrak{S}_i on one-dimensional spatial domains. These subsystems of port-Hamiltonian type are interconnected via boundary control and observation and are allowed to be of distinct port-Hamiltonian orders NiNN_i \in \mathbb{N}. Wellposedness and stability results for port-Hamiltonian systems of fixed order NNN \in \mathbb{N} are thereby generalised to networks of such. The abstract theory is applied to some particular model examples.Comment: Submitted to: Control Theory of Infinite-Dimensional System. Workshop on Control Theory of Infinite-Dimensional Systems, Hagen, January 2018. Operator Theory: Advances and Applications. (32 pages, 5 figures

    Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

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    In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in Japa

    Dissipative Stabilization of Linear Systems with Time-Varying General Distributed Delays (Complete Version)

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    New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying delay is continuous and bounded, we assume it to be bounded and measurable. Furthermore, the distributed delay kernels can be any square-integrable function over a bounded interval, where the kernels are handled directly by using a decomposition scenario without using approximations. By constructing a Krasovski\u{i} functional via the application of a novel integral inequality, sufficient conditions for the existence of a dissipative state feedback controller are derived in terms of matrix inequalities without utilizing the existing reciprocally convex combination lemmas. The proposed synthesis (stability) conditions, which take dissipativity into account, can be either solved directly by a standard numerical solver of semidefinite programming if they are convex, or reshaped into linear matrix inequalities, or solved via a proposed iterative algorithm. To the best of our knowledge, no existing methods can handle the synthesis problem investigated in this paper. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.Comment: Accepted by Automatic

    Incremental-dissipativity-based output synchronization of dynamical networks with switching topology

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    This paper studies asymptotic output synchronization for a class of dynamical networks with switching topology whose node dynamics are characterized by a quadratic form of incremental-dissipativity. The output synchronization problem of the switched network is first converted into a set stability analysis of a nonlinear dissipative system with a particular selection of input-output pair, which is related to special features of interconnected incremental-dissipative systems. Then, synchronization by designing switching among subnetworks, where none of them is self-synchronizing, is investigated by using the single Lyapunov function method. Algebraic synchronization criteria are established, and the results are applied to investigate synchronization of coupled biochemical oscillators. © 2014 IEEE.published_or_final_versio
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