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Proper feedback compensators for a strictly proper plant by polynomial equations

Frank Callier, Ferdinand Kraffer (2005)

International Journal of Applied Mathematics and Computer Science

We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction...

Properties of set-valued stochastic integrals

Jerzy Motyl, Joachim Syga (2006)

Discussiones Mathematicae Probability and Statistics

We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.

Protector control: Extension to a class of nonlinear distributed systems

Youssef Qaraai, Abdes Samed Bernoussi (2010)

International Journal of Applied Mathematics and Computer Science

We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a...

Pullback incremental attraction

Peter E. Kloeden, Thomas Lorenz (2014)

Nonautonomous Dynamical Systems

A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.

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