On pole assignment in multi-input controllable linear systems

It is shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed-loop system, formed by means of suitable linear feedback of the state. As an application of this result, it is shown that an open-loop system can be stabilized by linear feedback if and only if the unstable modes of its system matrix are controllable. A dual of this criterion is shown to be equivalent to the existence of an observer of Luenberger's type for asymptotic state identification.     

On pole structure assignment in linear systems

The problem of pole structure assignment (PSA) by state feedback in implicit, linear and uncontrollable systems is discussed in the article. It is shown that the problem is solvable if the system is regularisable. Then necessary and sufficient conditions for characteristic polynomial assignment are established. In the case of PSA (invariant polynomials assignment) just necessary conditions have been obtained. But it turns out that these conditions are also sufficient in some special cases. This happens, for example, when the system does not possess any non-proper controllability indexes. A possible application of the achieved results to modelling a constrained movement of a robot arm is outlined, too.     

On pole assignment in linear systems with incomplete state feedback

The following system is considered:dot{x}= Ax + Buy = Cxwherexis annvector describing the state of the system,uis anmvector of inputs to the system, andyis anlvector (l leq n) of output variables. It is shown that if rankC = l, and if (A,B) are controllable, then a linear feedback of the output variables u = K^*y, where K^*is a constant matrix, can always be found, so thatleigenvalues of the closed-loop system matrix A + BK^*C are arbitrarily close (but not necessarily equal) tolpreassigned values. (The preassigned values must be chosen so that any complex numbers appearing do so in complex conjugate pairs.) This generalizes an earlier result of Wonham [1]. An algorithm is described which enables K^*to be simply found, and examples of the algorithm applied to some simple systems are included.     

Comments on "A pole assignment algorithm for multivariable control systems"

In the above paper, the authors claim to have presented an algorithm which constitutes "a simple way of assigning poles." However, it is demonstrated by the presentation of a counterexample that this algorithm leads to erroneous results.     

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.     

Simultaneous pole assignment in linear periodic systems byconstrained structure feedback

The authors present methods for pole assignment by feedback with constrained structure in linear periodic systems using generalized sampled-data hold functions (GSHF). Constrained structure is taken to mean that the input of each channel is restricted to depend only on the measurements of some specific output channels. The basic idea of GSHF control is to use sample and hold, but to consider the hold function as a design parameter. Four strategies are proposed for closing a control loop using GSHF. The key to the results obtained is that, when GSHF control with constrained structure is applied to a periodic system, a discrete-time time-invariant, decentralized system is obtained for which control design methods are available     

Note on the pole assignment of q-dimensional linear systems

The method in Chu (1986) for the solution of the pole assignment problem of separable 2-D linear discrete systems with state feedback is improved and extended to q-D linear discrete systems and systems with output feedback.     

A computational algorithm for pole assignment of linear multiinput systems

An efficient computational algorithm for pole assignment of linear multiinput systems is proposed. A preliminary stage of the algorithm is a reduction of the system matrices into orthogonal canonical form. The gain matrix elements are then found by orthogonal transformation of the closed-loop system matrix into upper quasi-triangular form whose diagonal blocks correspond to the desired poles. The algorithm is numerically stable, the computed gain matrix being exact for a system with slightly perturbed matrices. It works equally well with real and complex, distinct, and multiple poles and is applicable to ill-conditioned and high-order problems.     

Comments on "On blocking zeros in linear multivariable systems"

It is suggested that the name "blocking zeros" in the above technical note is not appropriate and should be changed in order to avoid confusion in the literature.     

Robust stability and robust pole assignment of linear systems withstructured uncertainty

Sufficient conditions for the robust stability of linear time-varying systems are presented. The stability criteria are extended to the problem of the robust pole assignment of linear time-invariant systems to a specified region. These criteria, both for robust stability and robust pole assignment, improve some results in the literature. Examples are given to demonstrate the new criteria     

Comments on "Eigenstructure assignment in linear multivariable systems--A parametric solution"

The approaches to eigenstructure assignment in [1]-[3] and the above paper are shown to be equivalent.     

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.     

Sufficient conditions for generic simultaneous pole assignment andstabilization of linear MIMO dynamical systems

It has been shown that a generic r-tuple of m input p output dynamical systems is simultaneously stabilizable (pole assignable) if r相似文献   

On perturbations of linear controllable infinite-dimensional time-varying discrete-time systems

It is shown that for a broad class of linear (possibly time-varying and infinite-dimensional) discrete-time systems x_k+1 = A_kx_k + B_ku_k the property of being uniformly equicontrollable is preserved under small perturbations of system parameters. The problem of controllability of asymptotically time-invariant systems is also studied.     

Comments on "Structural identifiability in linear time-invariant systems"

The sufficiency feature of "sensitivity" identifiability is pointed out by showing that a linear time-invariant system is zero-state "sensitivity" identifiable only if it can be identified using a constant input. A necessary condition for local identifiability is given in terms of the "sensitivity" identifiablity.     

Comments on "Inversion of multivariable linear systems"

The purpose is to give a simple algebraic proof to the necessary part of the criterion of functional reproducibility of multivariable linear systems given by Silverman and to incorporate a slight correction to his criterion. Furthermore, the criteria of the functional reproducibility of Silverman and Sain and Massey [1] are shown to be equivalent.     

Robust pole assignment for systems with parameters

In this paper we investigate issues related to the control of linear multivariate systems which contain structured, parametric-type uncertainties. The objective is to construct parameter-independent proper compensators that provide ‘robust control’. Specifically, we consider the question of robust pole assignment. Systems are described by matrix fraction representations which involve a structured parametric form of uncertainty. We suggest conditions for robust pole assignability and demonstrate how to construct the required proper compensators. For the problem considered, we show that the class of systems which satisfy these conditions is quite large and we include results on generic solvability. The method is demonstrated by a physical example.     

An approach for pole assignment in singular systems

Pole assignment in a singular system Edx/dt=Ax+Bu is discussed. It is shown that the problem of assigning the roots of det(sE-(A +BF)) by applying a proportional feedback u=Fx+r in a given singular system is equivalent to the problem of pole assignment of an appropriate regular system. An immediate application of this result is that procedures and computational algorithms that were originally developed for assigning eigenvalues in regular systems become useful tools for pole assignment in singular systems. The approach provides a useful tool for the combined problem of eliminating impulsive behavior and stabilizing a singular system