Abstract: This paper presents a hybrid adaptive control scheme for assigning the closed loop poles of a single-input single-output continuous time linear system. The resulting closed loop system is shown to be globally stable when driven by an external reference signal containing exactly 2n distinct sinusoids where n is the open-loop system order. In particular, persistant excitation of the closed loop input-output data, and hence convergence of a sequential least squares identification algorithm is proven.

Abstract: This paper describes a technique to design a constant state feedback control law for a multi-input, multi-output, linear time-invariant model of a dynamic system such that the poles and the variant zeros of the closed loop system are placed at prespecified and distinct locations, defined via a desired transfer function matrix. The properties associated with the inverse of transfer function matrices and the conditions for the existence of the control law have been exploited.

Abstract: This paper studies the design of proper compensators to achieve arbitrary denominator matrices in the unity feedback configuration. The problem is first transformed into a set of linear algebraic equations. Some conditions for the existence of proper compensators are then developed. The design is achieved by solving the set of linear algebraic equations and is believed to be much simpler than the existing design methods.

Abstract: In this paper we investigate the problem of arbitrarily assigning the closed loop poles of a linear time invariant multivariable system with a proper output feed-back compensator in a manner which is insensitive with respect to parameters. We consider a certain parameter structure, define the notion of robust pole assignment and give necessary and/or sufficient conditions for accomplishing it.

Abstract: The paper considers a general state-space model of three-dimensional (3-D) systems, i.e. dynamic systems varying with respect to three independent variables. Two problems are studied and solved. The first problem is that of determining and computing the system transfer function matrix by using directly the state transition matrix of the given state-space model along with the system characteristic polynomial. This problem is solved through an extension of the well-known Fadeeva-Leverier algorithm to the 3-D case, and a transfer function computation formula is derived which can be implemented in an iterative way. The second problem is that of factorising the transfer function of single-input single-output systems via state-variable feedback. This problem is solvable under certain conditions only if the numerator of the open-loop transfer function is by itself factorisable in three 1-D polynomials. Otherwise the factorisation is restricted to the denominator of the closed-loop transfer function. The factorisation algorithm derived provides the state-feedback gain vector through the solution of a set of algebraic equations. Two nontrivial examples are worked out, and an interpretation of the 3-D model of the paper for the case of an elliptic distributed-parameter system in 3-dimensional spatial domain is given.

Abstract: Certain researchers derive the time-variant transfer function of a digital filter by assuming its behavior at certain sampling points. Based upon the derived coefficients, the transfer function is implemented via a time-variant difference equation by assuming a "frozen-time" relationship between the transfer function and its difference equation. This paper derives the generalized transfer function for a class of time-variant difference equation and illustrates the difference between the frozen-time and the generalized transfer functions.

Abstract: The problem factorizing (separating) the transfer function of a given SISO 3-D discrete system, ie of a system depending on three independent variables, is considered. The 3-D system is assumed to be available in its transfer function representation, which is converted to a canonical state-space model by a simple inspection procedure. Then applying state-feedback to this canonical model we choose the feedback matrix gain (under certain conditions) such that the transfer function of the closed-loop system has the desireed factorized form, ie a product of three 1-D transfer functions each one being dependent on a single variable. The method is illustrated by a nontrivial numerical example.

Abstract: This paper relates the properties of the loop transfer function to the feedback properties of the closed loop system. The relationship is expressed using a parameterization of the singular value decomposition of the loop transfer function. Trade-offs and limits on the specification of these parameters are examined.

Abstract: The problem of estimating the transfer function of a linear, stochastic system is considered. The transfer function is parametrized as a black box and no given order is chosen a priori. This means that the model orders may increase to infinity when the number of observed data tends to infinity. The consistency and convergence properties of the resulting transfer function estimates are investigated. Asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase. It is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise-to-signal-ratio at that frequency multiplied by the number-of-estimatedparameters to number-of-data-points-ratio. This result is essentially independent of the model structure used.

Abstract: A new design technique for multivariable feedback systems is presented. In this approach, n —1 open-loop transfer functions at different inputs of the plant, with all other feedback paths closed, are specified in advance, and are achieved exactly. The nth open-loop transfer function is a by-product of the design process, such that the overall feedback system is stabilized. The design approach is fitted to solve problems in which the plant elements can have non-stable poles and non-minimum phase zeros. The design process is straightforward, no iterations are necessary, and the achieved design copes exactly with the design specifications. The gainbandwidths of the different lis and the overall loop gain l* might be constrained due to non-stable poles and zeros of the plant elements. Based on the obtained different loop gains, any input output matrix T can bo achieved with the aid of an appropriate prefilter matrix F.

Abstract: The problem of linear system decoupling is examined based on recent results on linear feedback. New insight is obtained, through which resolution of the decoupliug problem is accomplished by calculations, performed directly on the given transfer matrix. Computation of the decoupling compensators follows by easy constructions. The problem of feedback block decoupling with internal stability, is also formulated and resolved.