I. V. Gaishun

Canonical Forms of Linear Nonstationary Observation Systems with Quasidifferentiable Coefficients with Respect to Various Transformation Groups

We obtain conditions for the existence and suggest a method for the construction of canonical forms of linear differential observation systems with the use of arbitrary linear transformation groups on the basis of the technique of quasidifferentiation with respect to lower triangular matrices.

Quasidifferentiability and canonical forms of linear nonstationary observation systems

We suggest a new method for constructing the Frobenius canonical form for linear nonstationary observation systems. In this method, the conditions imposed on the coefficients are substantially weakened. This is achieved by the use of the technique of quasidifferentiation of the output variables.

Quasidifferentiability and observability of linear nonstationary systems

We suggest a method for studying the observability of linear nonstationary ordinary differential systems on the basis of the quasidifferentiability of the output variables with respect to some lower-triangular matrix. This approach permits one to weaken the smoothness requirement on the coefficients in the statement of observability criteria.

Stability of two-parameter discrete systems with nonnegative coefficients

For a shift operator in the space of bounded sequences, we prove an analog of the classical Perron theorem on the spectrum of a positive matrix, which is then used to study the asymptotic properties of two-parameter discrete systems with nonnegative coefficients.

Controllability of differential systems in differential rings

We present a number of properties of differential equations in a unital associative ring equipped with a derivation operation. The controllability problem is stated, and conditions for its solvability are established.

Interval and robust observability of discrete systems with interval coefficients

We derive conditions for robust and interval observability for some classes of interval discrete systems.

Interval and Robust Stability of Two-Parameter Discrete Systems with Interval Coefficients

For a two-parameter discrete system with interval coefficients, we obtain conditions for robust stability and stability in the sense of interval analysis. In the general case, these two notions of stability are distinct; however, they are equivalent under the assumption that the coefficients of the system are nonnegative.

Existence and a method for constructing canonical forms of linear time-varying control systems with scalar input

We suggest a method for constructing Frobenius canonical forms of linear time-varying systems of ordinary differential equations with scalar input. The method is based on the quasidifferentiability of the coefficients with respect to a specially constructed lower-triangular matrix. The use of quasidifferentiation rules permits substantially weakening the existence conditions for such forms.

Controllability of linear nonstationary systems with scalar input and quasidifferentiable coefficients

We suggest a method for studying the controllability of linear nonstationary systems of ordinary differential equations. The method is based on the quasidifferentiability of the coefficients with respect to a specially constructed lower-triangular matrix. This approach permits substantially weakening the well-known smoothness conditions imposed on the coefficients when stating controllability criteria.

Relationship between canonical forms of linear differential observation systems and canonical forms of their discrete approximations

We establish a relationship between the canonical form of a linear differential system and the canonical form of its discrete approximation based on the replacement of the derivative by Euler’s finite difference. We prove that if there exist limits of certain sequences of discrete functions constructed with the use of coefficients of the canonical form of the discrete system, then these limits define the canonical form of the differential system.