Conditions For Pole Assignment Research Articles

Selection of Decentralised Control Structures: Structural Methodologies and Diagnostics

The paper aims at formulating an integrated approach for the selection of decentralized control structures using a number of structural criteria aiming at facilitating the design of decentralised control schemes. This requires the selection of decentralisation structure that will allow the generic solvability of a variety of decentralised control problems, such as pole assignment by decentralised output feedback. The approach is based on the use of necessary and sufficient conditions for generic solvability and exact solvability of decentralised control problems. The generic solvability conditions lead to characterisations of inputs and outputs channel partitions. The exact solvability conditions use criteria on avoiding the presence of fixed modes, as well as necessary conditions for pole assignment, expressed in terms of properties of Plϋcker invariants and Markov type matrices. The structural approach provides a classification of desirable input and output partitions based on structural criteria and it is embedded in an overall framework that may involve aspects related to large scale design.

Output Feedback Pole Assignment for Transfer Functions with Symmetries

This paper studies the problem of pole assignment for symmetric and Hamiltonian transfer functions. A necessary and sufficient condition for pole assignment by complex symmetric output feedback transformations is given. Moreover, in the case where the McMillan degree coincides with the number of parameters appearing in the symmetric feedback transformations, we derive an explicit combinatorial formula for the number of pole assigning symmetric feedback gains. The proof uses intersection theory in projective space as well as a formula for the degree of the complex Lagrangian Grassmann manifold.

A necessary condition for pole assignment by constant output feedback

In this paper we shall investigate the pole assignment problem by constant output feedback using transfer function techniques. In particular, a necessary condition is given for the existence of constant output feedback which assigns the eigenvalues of closed-loop system to any desired positions.

On pole assignment of linear systems by gain output feedback

In this paper, the Geometric Approach is used to derive in a straightforward way a sufficient condition for pole assignability by gain output feedback. This result leads to a pole assignment procedure which reduces to solving a system of min ( n - m, n - p) polynomial equations where n is the number of states, m the number of inputs, p the number of outputs. In the case where m + p > n, this system clearly appears to be linear. The degrees of freedom related to the pole assignment problem are expressed in terms of (right or left) eigenvectors.

Pole assignment and minimal feedback design†

The problem of pole assignment is considered for three types of output feedback configurations : a combination of dynamic precompensation and dynamic output feedback : dynamic precompensation and unity output feedback ; and pure dynamic output feedback. In all three cases, the conditions for pole assignment depend on certain integer invariants which are determined, roughly speaking, by the unstable poles, by the unstable zeros, and by the zeros at infinity of the transfer matrix of the given system. †This research was supported in part by US Army Research Grant DAA29-80-C0050 and US Air Force Grant AFOSR76-3034D through the Center for Mathematical System Theory, University of Florida, Gainesville, Florida 32611, U.S.A.

Pole assignment by piecewise constant output feedback

The problem of polo assignment by piecewise constant output feedback is considered for linear time-invariant systems with infrequent observation. An algorithm for computing the output feedback gain is presented, together with necessary and sufficient conditions for pole assignment. The resultant output feedback gain is a periodic piecewise constant function of time.