Pole placement for singular systems

Finite eigenvalue assignment for a descriptor system

“…This result cannot be obtained using the methods presented, for example, in [6,7]. CONCLUSIONS An effective method is presented for assigning the finite eigenvalues of a linear descriptor dynamical sys tem.…”

“…Then (7) can be represented as (1), and let be a nonsingular matrix. Then (7) can be represented in a form equivalent to (8), namely,…”

“…Without loss of generality, we assume that system (1) is completely controllable [4][5][6][7][8] and the generalized matrix pencil λE -A, which characterizes the dynam ical properties of the free (natural) motion of system (1), has m finite eigenvalues (poles) and (n -m) infinite eigenvalues. The same property system (1) expressed equiva lently in terms of finite eigenvalues is related to the corresponding set of the pair of matrices (E, A) and is formally given by (2) Loosely speaking, finite eigenvalues (poles) can be associated with the number differential or difference equations, while infinite eigenvalues, with the number of algebraic equations in system (1).…”

“…This problem is known as pole placement or eigen value assignment and has been extensively studied in various formulations [1][2][3][4][5][6][7][8].…”

Fault-tolerant Control of Discrete-time Descriptor Systems using Virtual Actuators

“…In a descriptor system, some state variables are related algebraically and, consequently, the mathematical formulation is a set of coupled differential and algebraic equations, which include information on both the static and the dynamical constraints of a plant [10]. Descriptor systems have been investigated thoroughly during the last decades, and several results of theoretical and practical relevance have been obtained, such as stabilization [11], pole assignment [12], linear-quadratic optimal control [13] and observer design [14].…”