Systems & Control Letters 

Abstract: The stability and stabilization of a grey system whose state matrix is triangular is studied. The displacement operator and established transfer developed by the author are the indispensable tool for the grey system.

Abstract: Let Wt; t ϵ [0, 1] be a standard k-dimensional Weiner process defined on a probability space ( Ω, F, P ), and let Ft denote its natural filtration. Given a F1 measurable d-dimensional random vector X, we look for an adapted pair of processes {x(t), y(t); t ϵ [0, 1]} with values in Rd and Rd×k respectively, which solves an equation of the form: x(t) + ∫ t 1 f(s, x(s), y(s)) ds + ∫ t 1 [g(s, x(s)) + y(s)] dW s = X. A linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process. We also generalize our results to the following equation: x(t) + ∫ t 1 f(s, x(s), y(s)) ds + ∫ t 1 g(s, x(s)) + y(s)) dW s = X under rather restrictive assumptions on g.

Abstract: We consider the problem of finding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of finding the fastest converging linear iteration can be cast as a semidefinite program, and therefore efficiently and globally solved. These optimal linear iterations are often substantially faster than several common heuristics that are based on the Laplacian of the associated graph. We show how problem structure can be exploited to speed up interior-point methods for solving the fastest distributed linear iteration problem, for networks with up to a thousand or so edges. We also describe a simple subgradient method that handles far larger problems, with up to 100 000 edges. We give several extensions and variations on the basic problem.

Abstract: We show that the well-known Lyapunov sufficient condition for "input-to-state stability" (ISS) is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.

Abstract: A new robust stability condition for uncertain discrete-time systems with convex polytopic uncertainty is given. It enables to check stability using parameter-dependent Lyapunov functions which are derived from LMI conditions. It is shown that this new condition provides better results than the classical quadratic stability. Besides the use of a parameter-dependent Lyapunov function, this condition exhibits a kind of decoupling between the Lyapunov and the system matrices which may be explored for control synthesis purposes. A numerical example illustrates the results.