On the assignability of regularity coefficients and central exponents of discrete linear time-varying systems

In this paper we investigate the problem of assignability of the so-called regularity coefficients and central exponents of discrete linear time-varying systems. The main result presents a possibility of assignability of Lyapunov, Perron, Grobman regularity coefficients and central exponents by a linear time-varying feedback under the assumptions of uniform complete controllability

On Lyapunov and Upper Bohl Exponents of Diagonal Discrete Linear Time-Varying Systems

In this paper the necessary and sufficient conditions for two given functions to be the Lyapunov and the upper Bohl exponents of a certain discrete linear system with diagonal coefficients are presented. The obtained conditions are described in terms of easily verifiable properties

Continuity of Solutions of Riccati Equations for the Discrete-Time Jlqp

The continuity of the solutions of difference and algebraic coupled Riccati equations for the discrete-time Markovian jump linear quadratic control problem as a function of coefficients is verified. The line of reasoning goes through the use of the minimum property formulated analogously to the one for coupled continuous Riccati equations presented by Wonham and a set of comparison theorems

On Adaptive Control for the Continuous Time-varying JLQG Problem

In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated through strongly consistent estimators

Some properties of the spectral radius of a set of matrices

In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the existing results it is expressed by eigenvalues

Falseness of the finiteness property of the spectral subradius

We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive because we do not show any explicit value of α that has described property. The problem of finding such values is still open