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The focus in this paper is analysis of stability and controller design for interconnected systems. This includes both the case with known and unknown interconnected sub-system. The key element in both the stability analysis and controller design is the application of the Youla-Jabr-Bongiorno-Kucera (YJBK) parameterization. The dual YJBK transfer function is applied in connection with the closed-loop...
We propose a compositional stability analysis framework for verifying properties of systems that are interconnections of multiple subsystems. The proposed method assembles stability certificates for the interconnected system based on the certificates for the input-output properties of the subsystems. The decomposition in the analysis is achieved by utilizing dual decomposition ideas from optimization...
We consider networks of input-to-state dynamically stable (ISDS) systems and provide a small gain condition under which the entire network is again ISDS. A Lyapunov formulation of the nonlinear small gain theorem for two interconnected ISDS systems is proved. It provides a constructive method to find an ISDS Lyapunov function for such an interconnection.
This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain theorem for operators is examined. The result developed for operators allows applications to a wide class of systems, including state space systems with delays.
This paper examines the stability of quantum feedback networks. We introduce a novel characterization, in terms of equivalence classes of operators, that may be used to describe open quantum systems. In this characterization, equivalence classes of operators are shown to be elements of a Banach space such that the norm of an operator is analogous to the root mean square expectation value of the operator...
This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain...
This paper provides synchronization conditions for networks of nonlinear systems, where each component of the network itself consists of subsystems represented as operators in the extended L2 space. The synchronization conditions are provided by combining the input-output properties of the subsystems with information about the structure of network. The work is motivated by cellular networks where...
This paper considers networks consisting of integral input-to-state stable (iISS) subsystems and addresses the problem of verifying iISS property of a given network. First, we focus on construction of continuously differentiable Lyapunov functions, and derive a condition ensuring the iISS of the network comprising n subsystems. Although this approach referred to as the sum-type construction has not...
It is important content that the studying connective stability among the stability studying of the large-scale interconnected systems. The many results recently have been given for the normal systems, the studying result of the singular large scale systems, however, is a little. The paper discussed the connective stability of a kind of nonlinear singular large-scale dynamical systems by means of singular...
We consider the problem of model order reduction for spatially-varying interconnected systems distributed in one spatial dimension. The sequentially semi-separable matrix structure of such systems can be exploited to allow efficient structure preserving model order reduction using the matrix sign function. Iterative algorithms are provided for fast computation, which is demonstrated on an example.
In this paper we develop dissipativity theory for discontinuous dynamical systems. Specifically, using set-valued supply rate maps and set-valued connective supply rate maps consisting of locally Lebesgue integrable supply rates and connective supply rates, respectively, and set-valued storage maps consisting of piecewise continuous storage functions, dissipativity properties for discontinuous dynamical...
Safety-critical control systems use fault tolerant interconnections of components to minimize the effect of randomly triggered faults. The system availability process indicates whether or not the interconnection is operating correctly at each time instant. It is a 2-state process that results from the transformation of the stochastic processes characterizing the availability processes of the interconnected...
In this paper, a decentralized overlapping static output feedback law is proposed to control a linear time-invariant (LTI) interconnected system. It is assumed that an overlapping information flow structure is given which determines which output measurements are available for any local control agent. Uncertain transmission delay is also considered in communication links among different subsystems...
In this paper, we study the stability (convergence time) of an interconnected dynamical system with respect to its connectivity in the presence of delayed feedbacks sensory inputs/outputs data. In particular, we show that under some conditions, that we introduce and present in this paper, related to the interconnected links time-delays, the less connected a given dynamical system is, the longer it...
This paper deals with decentralized stabilization of nonlinear systems composed of interconnected Takagi-Sugeno fuzzy descriptors. To ensure the stability of the overall closed-loop system, a set of decentralized Parallel Distributed Compensations (PDC) controllers is employed. The stability conditions are then derived into Linear Matrix Inequalities (LMI) using a fuzzy Lyapunov function for less...
Numerically tractable conditions for input-to-state stability (ISS) analysis are given for a class of nonlinear systems. These conditions originate from ISS inequalities for the cascade connection of the systems and the feedback interconnected system. If class of the systems is restricted such as polynomial ones, then it is possible to avail recent developed sum of squares relaxation of positive polynomials...
This paper deals with a hierarchical consensus problem in large scale systems. We first define the hierarchical consensus and propose a fairly general model of the system. We then define the interconnection matrix which expresses interconnection property between layers, where we focus on the rank of this matrix. In order to examine the relationship between the rank of interconnection matrix and stability...
In this paper. a decomposition approach is investigated for stabilization and control of composite linear time-invariant multivariable systems. The control inputs to the various subsystems are assumed to be independent and uncoupled. A sufficient condition is derived to ensure the stability of the composite system provided that all its subsystems are stable.
In the present paper the problem of vibration suppression in segmented reflector telescopes is considered. The decomposition of the structure into smaller components is discussed and control laws for vibration suppression as well as conditions for stability at the local level are derived. These conditions, and the properties of the interconnecting patterns are then utilized to obtain sufficient conditions...
We present a deterministic design approach for decentralized robust controls of large-scale nonlinear uncertain dynamical systems. Two important types of robust control design are drawn. The local design makes use of the local state of each subsystem as the feedback information. The global design utilizes the local state as well as the neighboring states as the feedback information. Only the set of...
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