STABILIZABILITY OF LINEAR-SYSTEMS USING DISCRETE FEEDBACK

The eigenvalue assignment problem of a controllable continuous linear system using continuous and discrete feedback loops is discussed. It is shown that for a given set of distinct self-conjugate complex numbers included inside of the unit circle, and for an arbitrarily given value of the sampling frequency (in the discrete feedback loop), it is possible to choose constant feedback matrices such that eigenvalues of the matrix of dynamics of the closed-loop system are located sufficiently near to appropriate numbers of the given set of complex numbers. The obtained result may immediately be applied in the case of discrete linear systems with sampling of the input signal and continuous state feedbacks.