Pole assignment for uncertain systems in a specified disk by output feedback

In this paper the problem of pole assignment in a disk by output feedback for continuous-or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given.     

Pole assignment in a specified disk

The problem of assigning all poles of a closed-loop system in a specified disk by state feedback is considered for both continuous and discrete systems. A state feedback control law is determined by using a discrete Riccati equation. This kind of pole assignment problem is namedD-pole assignment, and its relation to the optimal control problem and its robustness properties are discussed. The gain and phase margins for all closed-loop poles to stay inside the specified diskDare determined for the proposed control.     

Pole assignment of linear uncertain systems in a sector via aLyapunov-type approach

The problem of designing robust control laws, in performance and in stability, for uncertain linear systems is considered. Performances are taken into account using root clustering of the closed-loop dynamic matrix in a sector of the complex plane. A synthesis procedure, based on a sufficient condition for quadratic stabilization and root clustering, such as stabilizability, is given, using an auxiliary convex problem. The results are illustrated by a significant example from the literature     

Pole assignment for distributed systems by finite-dimensional control

The question of pole assignment for a class of distributed systems by means of finite dimensional control is considered. A finite dimensional compensator is usually designed based on a reduced order model, and it is not a priori known what effect this will have on the original infinite dimensional system. Explicit formulas are derived which enable one to calculate the eigenvalues of the resulting closed loop system. For a certain compensator design, estimates are derived which can be used to guarantee stability a priori. Numerical results are also presented.     

Globally convergent algorithms for robust pole assignment by statefeedback

It is observed that an algorithm proposed in 1985 by Kautsky, Nichols, and Van Dooren (KNV) amounts to maximizing, at each iteration, the determinant of the candidate closed-loop eigenvector matrix X with respect to one of its columns (with unit-length constraint), subject to the constraint that it remains an achievable closed-loop eigenvector matrix. This interpretation is used to prove convergence of the KNV algorithm. It is then shown that a more efficient algorithm is obtained if det (X) is concurrently maximized with respect to two columns of X, and such a scheme is easily extended to the case where the eigenvalues to be assigned include complex conjugate pairs. Variations exploiting the availability of multiple processors are suggested. Convergence properties of the proposed algorithms are established. Their superiority is demonstrated numerically     

Pole assignment for systems over rings

A very simple proof of the pole assignment theorem for systems over a principal ideal domain (and other rings) is given. Furthermore, an algorithm is presented. Extensions are also indicated.     

Pole assignment for linear periodic systems by memoryless outputfeedback

We consider linear periodic discrete-time systems. We are interested in the problem of placing the poles of the monodromy map by means of periodic output feedback of the same or multiple period. It is well known that, in general, the poles of time-invariant systems cannot be assigned by constant output feedback. This is in contrast with what can be obtained in the context of time-variant systems. The main contribution of this paper is that periodic output feedback suffices for pole placement of periodic systems     

Robustness of pole assignment in a specified region for perturbed systems

This paper deals with the pole location of a perturbed matrix A + E. Two perturbation classes are discussed: one with structured perturbations |E| ≤ U (a given non-negative matrix) and one where only the spectral norm ||E|| is given. Sufficient conditions are derived for the eigenvalues of A + E to be located within a circle C(α, r). The case of a diagonalizable matrix A is also considered and a sufficient condition for robust stability of a class of perturbed discrete systems is derived. Numerical examples are presented for illustration.     

Pole assignment in a specified circular region using a bilinear transformation onto the unit circle

An algorithm for pole assignment in a specified circular region using a bilinear transformation onto the unit circle is considered, A Lyapunov type test is developed to check that all the eigenvalues of a discrete system are within a circle in the complex plane. Pole placement in a circular region by LQ state feedback design is investigated for discrete linear systems. Perturbation bounds are derived, using bilinear transformation, for all closed-loop poles of a perturbed discrete system to remain inside a specified circular region. Illustrative examples are included     

Regional pole assignment for uncertain delta-operator systems

The pole assignment in a specified disk by state feedback for uncertain delta-operator systems is studied. By making use of algebra Riccati equations, a sufficient and necessary condition of pole assignment for a kind of parameter uncertain delta-operator system in a specified disk by state feedback is presented. And the design method of state feedback controller is also developed.The proposed method can unify some previous rehted results of continuous and discrete time systems into the delta framework. The efficiency of the design method is illustrated by a numerical example.     

Pole assignment for linear time-invariant systems by periodic memoryless output feedback

It is well known that the poles of a linear time-invariant controllable and observable system can be assigned arbitrarily by state feedback. When only the output is available, pole assignment is still possible by means of dynamic output feedback. In this paper the potential of time-varying memoryless output feedback is considered. It is shown that, up to some technical conditions, it is indeed possible to allocate the poles of a linear time-invariant discrete-time system by memoryless output feedback with periodic gains. The period of the gains is (n + 1) with n the order of the system. The power of the design technique is proved to be comparable to what can be achieved by the classical dynamic feedback approach.     

Robustness of pole assignment in a specified circular region for discrete-time grey systems

New sufficient conditions are proposed to guarantee robust pole location within a specified circular region for a discrete-time grey system. By mathematical analysis, the proposed new approach is proved to be less conservative than the existing technique reported in the literature. The proposed method, instead of solving the Lyapunov matrix equation, requires only the simple computation of the spectral radius of a non-negative matrix. Examples are given to demonstrate the use of the proposed method and to illustrate the improvement in that method.     

Pole assignment for multi-input multi-output systems using output feedback

In this paper the problem of pole assignment using constant gain output feedback is studied for MIMO system with system order n > m + l − 1, where m and l are the number of inputs and outputs, respectively. A new procedure is presented to design a constant gain output feedback matrix which assigns (m + l − 2) poles exactly to the desired locations and shifts all the unassigned poles to suitable locations using root locus techniques.     

A note on pole assignment in uncertain systems

A new method for full-rank state-feedback pole assignment is introduced. A particular advantage of this method is that no freedom in the design parameters is lost. Hence, further design problems such as robust pole assignment in uncertain systems are alleviated. An application of this feature is shown for a particular linear model of the F16 aircraft. The connections between state feedback and several concepts in the literature such as incomplete input feedback, incomplete state feedback, output feedback and incomplete pole assignment are also given.     

Output feedback disk pole assignment for systems with positive realuncertainty

In this paper, the problem of pole assignment in a disk by output feedback for continuous or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given. Some related problems are also discussed     

Pole assignment in linear time-invariant multivariable systems with constant disturbances

Necessary and sufficient conditions are derived for a minimal order realizable, linear, time invariant differential feedback control system to exist for a linear time-invariant system with constant unknown disturbances, such that the eigenvalues of the closed-loop system take on pre-assigned values in the left hand part of the complex plane and such that the outputs of the system tend to zero as t → ∞. Some numerical examples are included to illustrate the result.     

Pole assignment by state transition graph

The pole assignment problem is considered, using the graph representation of a matrix. The parametrization of controllers which have a specified characteristic polynomial is given. A simple algorithm based on graphs is presented and two examples are given