E. Emre

Regulation of split linear systems over rings: Coefficient-assignment and observers

A theory of regulators is developed for finite-free split linear systems over a commutative ring K . This is achieved by developing a theory, of coefficient-assignment and observers. It is shown that the problem of coefficient-assignment can be solved for reachable systems by using dynamic state feedback. For strongly observable systems, it is shown that observers with arbitrary dynamics can be constructed. Internal stability of observer and state feedback configuration is considered explicitly. Some examples are given to illustrate these techniques.

Simultaneous stabilization with fixed closed-loop characteristic polynomial

A solution is given to the problem of simultaneously stabilizing m single-input-single-output plants by one dynamic compensator with the constraint that each closed-loop system has the same characteristic polynomial.

Control of linear systems with fixed noncommensurate point delays

The First solution is given to the fundamental open problem of stabilizability and detectability (necessary sufficient conditions for internal stabilization by feedback) of retarded and a large class of neutral delay-differential systems with several fixed, noncommensurate point delays, using causal compensators (observers and state-feedback or dynamic output feedback), which are also the same type of neutral or retarded delay-differential systems with fixed point delays only. Our results are rank conditions on the system matrices [ zI - F:G ] and [ zIF^{T}:H^{T} ] evaluated at points in the complex plane and are the weakest possible generally applicable sufficient such rank conditions for stabilization of neutral systems in the light of what is known on the stability of such systems. These conditions are necessary for most practical purposes. The class of systems we consider includes all retarded delay-differential systems with noncommensurate, fixed point delays. In the case of retarded systems, these rank conditions are necessary and sufficient conditions for stabilization via compensators which are causal retarded delay-differential systems with fixed point delays only. These constitute the first full solution of these previously unsolved problems of stabilizability and detectability (which, together, are necessary and sufficient conditions for internal stabilization by feedback) for delay-differential systems even in the retarded single fixed point delay case. An application of our results to a problem of practical importance in control of linear systems with no delays provides a stabilization criterion interesting in itself.

Minimal dynamic inverses for linear systems with arbitrary initial states

In this short paper the problem of finding a minimal left inverse of a linear time-invariant system for nonzero initial conditions is considered. It is shown that this problem is equivalent to finding a minimal dynamical cover. As a result of this, the minimal inverse problem can be solved immediately using the previous results on dynamic covers. No restriction other than invertibility is assumed on the original system.

Further results on polynomial characterizations of ( F, G )-invariant and reachability subspaces

This paper is concerned with further development of the unification between polynomial matrix and geometric theories of linear systems following the work of Emre and Hautus. Equivalence between different polynomial characterizations of ( F, G )-invariant and reachability subspaces is shown explicitly. Several new results are given which clarify the relations between the polynomial system matrix, invariant subspaces, and system zeros. Finally, a polynomial characterization of and a constructive procedure to obtain the largest stabilizability subspace in ker H are given.

Transfer matrices, realization, and control of continuous-time linear time-varying systems via polynomial fractional representations

Abstract An algebraic theory of transfer matrices, fractional representations, and control for linear continuous-time time-varying systems based on the realization theory of input-output maps is given. It is shown for the first time that the realization of such systems specified by an abstract input-output map (as a module homomorphism over noncommutative polynomial rings) can be established using an abstract Kalman input-output map defined over a ring of skew polynomials with time-varying coefficients. It is shown that, in fact, transfer matrices can be defined as formal power

Extended solution to multiple maneuvering target tracking

An improved algorithm for tracking multiple maneuvering targets is presented. This approach is implemented with an approximate adaptive filter consisting of the one-step conditional maximum-likelihood technique together with the extended Kalman filter and an adaptive maneuvering compensator. In order to avoid the extra computational burden of considering events with negligible probability, a validation matrix is defined in the tracking structure. With this approach, data-association and target maneuvering problems can be solved simultaneously. Detailed Monte Carlo simulations of the algorithm for many tracking situations are described. Computer simulation results indicate that this approach successfully tracks multiple maneuvering targets over a wide range of conditions. >

Generalized model matching and (F,G)-invariant submodules for linear systems over rings

Abstract A generalized version of the exact model matching problem (GEMMP) is considered for linear multivariable systems over an arbitrary commutative ring K with identity. Reduced forms of this problem are introduced, and a characterization of all solutions and minimal order solutions is given, both with and without the properness constraint on the solutions, in terms of linear equations over K and K -modules. An approach to the characterization of all stable solutions is presented which, under a certain Bezout condition and a freeness condition, provides a parametrization of all stable solutions. The results provide an explicit parametrization of all solutions and all stable solutions in case K is a field, without the Bezout condition. This is achieved through a very simple characterization and a generalization to an arbitrary field K of the “fixed poles” of the model matching problem in terms of invariant factors of a certain polynomial matrix. The results also show that whenever the GEMMP has a solution, there exist solutions whose poles can be chosen arbitrarily as far as they contain the “fixed poles” with the right multiplicities (in the algebraic closure of K ). Implications of these results in regard to inverse systems are shown. Equivalent simpler forms (in state space form) of the problem are shown to be obtainable. A theory of finitely generated ( F , G )-invariant submodules for linear systems over rings is developed, and the geometric equivalent of the model matching problem—the dynamic cover problem—is formulated, to which the results of the previous sections provide a solution in the reduced case.

Pole placement for linear systems over Bezout domains

The problem of pole placement for linear systems over rings is considered. For a class of rings, our results show that one can construct reduced-order dynamic output feedback compensators for pole placement. Our results also provide an alternative proof of some previously known results on the problem of pole placement by state feedback for a class of reachable pairs ( F,G ) over Bezout domains.

Systems over rings: Output regulation and tracking

The problems of output regulation and tracking with internal stability for systems defined over a class of rings is considered. For systems defined over a principal ideal domain the results for the usual finite dimensional systems generalize without appreciable change. For systems over a commutative ring with identity a sufficient condition has been obtained. The condition also becomes necessary under additional constraints on the problem data.