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We consider a linear time-invariant multivariable square control system. For this system, we are interested in the description of zero dynamics, that is, the dynamics of the system for the case of identically zero output. We study the case in which the relative degree is undefined for the system. [ABSTRACT FROM AUTHOR]

We consider the output stabilization problem for a linear time-independent system. We show that if the system output is zero, y( t) ≡ 0, then, for the stabilization of the entire state vector, the sufficient condition of stability of the zero dynamics can be replaced by the boundedness of the system input (provided that the characteristic polynomial of the zero dynamics has no eigenvalues on the imaginary axis). [ABSTRACT FROM AUTHOR]

Minimal stabilization is considered for a scalar system. The minimal stabilization problem is shown to be equivalent to the problem of intersecting the space of stable polynomials with a linear manifold. It is proved that the linear manifold can be described by a linear system of algebraic equations with Hankel structure. The article provides examples of some applications of the minimal stabilizer search algorithm. [ABSTRACT FROM AUTHOR]

We consider the problem of inversion of a dynamical system, that is, the problem of real-time reconstruction of the unknown input of the system on the basis of measurements of its output. We consider linear systems of functional-differential equations in the case of commensurable delays. We obtain necessary conditions for the invertibility of this class of systems and suggest an inversion algorithm that permits one to obtain an estimate of the unknown input signal with given accuracy. [ABSTRACT FROM AUTHOR]

We consider the problem of constructing a stabilizer described by a system of linear differential equations and such that a given dynamical system becomes stable after being closed by the feedback produced by the stabilizer. Moreover, we require that the dimension of the stabilizer, that is, the dimension of its state vector, be minimal. We assume that the given system has either a single input and multiple outputs (a SIMO system) or, on the opposite, multiple inputs and a single output (a MISO system). [ABSTRACT FROM AUTHOR]

We consider the problem on the existence of a common stabilizing controller for a finite family of linear vector dynamical systems. A sufficient condition, obtained on the basis of topological methods, is presented for the existence of a common stabilizer. Constructive approaches to the development of an algorithm for verifying this condition are indicated. [ABSTRACT FROM AUTHOR]

We consider the stabilizer synthesis problem for linear stationary control dynamical systems; attention is mainly focused on the investigation of possibilities to reduce the order of such stabilizers. The problem is considered in two settings. The first setting deals with the construction of stabilizers of given order (in particular, the minimum possible order); no conditions are imposed on the spectrum of the closed system. For scalar (single-input-single-output) control systems, we suggest an approach to the solution of this problem and obtain necessary and sufficient conditions for the existence of a stabilizer of a given order. The second problem is that of synthesizing a stabilizer of minimum order with given dynamic properties (a given spectrum or a given distribution of the spectrum of the closed system, in particular, with a guaranteed convergence rate of the closed system). For this problem, we suggest two approaches that permit one to obtain an upper bound for the dimension of such stabilizers. [ABSTRACT FROM AUTHOR]