197,493 research outputs found

    Stability of switched linear differential systems

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    We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching instants is specified by gluing conditions, i.e. algebraic conditions on the trajectories and their derivatives at the switching instant. We provide sufficient conditions for stability based on LMIs for systems with general gluing conditions. We also analyse the role of positive-realness in providing sufficient polynomial-algebraic conditions for stability of two-modes switched systems with special gluing conditions

    Applications of Linear Co-positive Lyapunov Functions for Switched Linear Positive Systems

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    In this paper we review necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for switched linear positive systems. Both the state dependent and arbitrary switching cases are considered and a number of applications are presented

    On switched Hamiltonian systems

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    In this paper we study the well-posedness and stability of a class of switched linear passive systems. Instrumental in our approach is the result, also of interest in its own right, that any linear passive input-state-output system with strictly positive storage function can be written as a port-Hamiltonian system

    On the D-Stability of Linear and Nonlinear Positive Switched Systems

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    We present a number of results on D-stability of positive switched systems. Different classes of linear and nonlinear positive switched systems are considered and simple conditions for D-stability of each class are presented

    Essentially Negative News About Positive Systems

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    In this paper the discretisation of switched and non-switched linear positive systems using Padé approximations is considered. Padé approximations to the matrix exponential are sometimes used by control engineers for discretising continuous time systems and for control system design. We observe that this method of approximation is not suited for the discretisation of positive dynamic systems, for two key reasons. First, certain types of Lyapunov stability are not, in general, preserved. Secondly, and more seriously, positivity need not be preserved, even when stability is. Finally we present an alternative approximation to the matrix exponential which preserves positivity, and linear and quadratic stability

    On positive-realness and Lyapunov functions for switched linear differential systems

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    We show new results about Lyapunov stability of switched linear differential systems (SLDS) using the concept ofpositive realness. The main results include stability conditions for a class of SLDS with augmented banks and the parametrization of families of asymptotically stable SLDS with three modes. Such conditions can be verified using LMIs that can be directly set up from the higher-order differential equations describing the mode

    On the preservation of co-positive Lyapunov functions under Padé discretization for positive systems

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    In this paper the discretization of switched and non-switched linear positive systems using Padé approximations is considered. We show: 1) first order diagonal Padé approximation preserves both linear and quadratic co-positive Lyapunov functions, higher order transformations need an additional condition on the sampling time1; 2) positivity need not be preserved even for arbitrarily small sampling time for certain Padé approximations. Sufficient conditions on the Padé approximations are given to preserve positivity of the discrete-time system. Finally, some examples are given to illustrate the efficacy of our results
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