Linear output feedback compensation of rank-one systems

A new method is presented for arbitrarily assigning the closed-loop poles of a linear multi-input/multi-output system using linear output feedback. The method employs a new notion of rank-one system representations and involves the use of state transformation matrices which preserve such representations while reducing the degree of the feedforward matrix     

Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment

This paper outlines a new geometric parameterization of 2D curves where parameterization is in terms of geometric invariants and parameters that determine intrinsic coordinate systems. This new approach handles two fundamental problems: single-computation alignment, and recognition of 2D shapes under Euclidean or affine transformations. The approach is model-based: every shape is first fitted by a quartic represented by a fourth degree 2D polynomial. Based on the decomposition of this equation into three covariant conics, we are able, in both the Euclidean and the affine cases, to define a unique intrinsic coordinate system for non-singular bounded quartics that incorporates usable alignment information contained in the polynomial representation, a complete set of geometric invariants, and thus an associated canonical form for a quartic. This representation permits shape recognition based on 11 Euclidean invariants, or 8 affine invariants. This is illustrated in experiments with real data sets.     

Parameter adaptive identification and control

A new parameter adaptive control scheme is outlined which essentially allows one to arbitrarily position all of the poles of an unknown, linear, scalar system of known dynamical order. The technique is based on identifying the parameters which characterize the dynamical behavior of the system in differential operator form and simultaneously implementing an adaptive observer which generates a feedback control signal which converges to the equivalent of an appropriate pole placing linear state variable control law. It is shown that the overall control configuration, consisting of a system identifier and a complementary adaptive observer, is globally stable provided only that the control input is "sufficiently rich" in frequency content. A study employing an unstable, nonminimum phase plant is presented to illustrate the technique.     

Arbitrary adaptive pole placement for linear multivariable systems

This paper presents a methodology for adaptively assigning the closed-loop poles of either continuous or discrete time linear mnltivariable systems. The scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified. Rather the control parameters, and an "equivalent" plant parameterization are simultaneously estimated from input-output data using linear parameter estimation procedures. Implementation of the scheme requires only knowledge of the system controllability indexes, and an upper bound on the observabilily index.     

A parameter adaptive control structure for linear multivariable systems

This paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous-time linear multivariable system represented by an (m times m) strictly proper transfer matrixT(s), providedT(s)has no right-half plane zeros. The controller parameters can be directly estimated from input-output data. The paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design. This information is a natural extension of that required in the scalar case.     

Parameter insensitive pole assignment for scalar input systems

Under the assumption that the parameters affect the systems "linearly," arbitrary partial insensitive pole placement problem for scalar input systems have been solved. A new definition for partial pole placement, which takes into account the effect of the unknown varying parameters in the system, has been used. The result is first given for a system with one parameter, and then, it is extended to systems with more than one parameter. The dual of the same result is also given. The paper also emphasizes the structural properties of systems with varying parameters.     

A division algorithm for polynomial matrices

A new algorithm is presented for directly determining both the quotient and the remainder associated with the division of one polynomial matrix by another. The procedure requires that the denominator matrix be column proper with nonzero column degrees. However, unlike earlier algorithms, only real matrix multiplications are employed; i.e., there is no need for matrix inversions, either explicit or implicit.     

On determining the zeros of state-space systems

The zeros of a linear, time-invariant, state-space system are defined, and a matrix rank test for determining their locus is formally established and illustrated by example.     

A general algorithm for determining state-space representations

A new and direct procedure is presented for determining state-space representations of given, time-invariant systems whose dynamical behavior is expressed in a more general, differential operator form. The procedure employs some preliminary polynomial matrix operations, if necessary, in order to “reduce” the given system to an equivalent differential operator form which satisfies four specific conditions. An equivalent state-space representation is then determined in a most direct manner; i.e. the algorithm presented requires only a single matrix inversion. An explicit relationship between the partial state and input of the given system and the state of the equivalent state-space system is also obtained.