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This paper deals with the computation of the Bezoutian using two dimensional discrete Fourier transform techniques. The Bezoutian is an important tool in the study of stability of systems, especially in localization of roots of a polynomial. This paper gives an alternate method to compute the Bezoutian. Results exploring the link between the Bezoutian and Lyapunov operator under suitable assumption...
Impulsive solutions in LTI dynamical systems have received ample attention, but primarily for descriptor systems, i.e., first order Differential Algebraic Equations (DAEs). This paper focuses on the impulsive behavior of higher order dynamical systems and analyzes the causes of impulses in the context of interconnection of one or more dynamical systems. We extend the definition of impulse-controllability...
We study Hamiltonian systems, namely, systems comprising of trajectories which are ‘stationary’ with respect to a quadratic performance index: they play a central role in many optimal control problems. A typical assumption in the literature is that of ‘regularity’: the resulting first-order dynamical system is a regular state space system and not a singular descriptor system. In this paper we show...
In this paper we study solutions to linear ordinary constant coefficient differential equations on the half-line and relate impulsive solutions to the pole/zero structure at infinity of an associated polynomial matrix. While this relation has been thoroughly studied for first order systems, and through first order analysis also for higher order systems partially, the use of the ‘state map’, in particular...
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