Predicting uncertainty in geometric fluid mechanics. Sub-Riemannian geometry and finite time thermodynamics Part 1: The stochastic oscillator. Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem. A survey of some aspects of dynamical topology: Dynamical compactness and Slovak spaces. Coordinate-independent criteria for Hopf bifurcations. Nonautonomous gradient-like vector fields on the circle: Classification, structural stability and autonomization.

Lev M. Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Effective Hamiltonian dynamics via the Maupertuis principle. Hartmut Schwetlick , Daniel C. Ferdinand Verhulst. Preface to this special issue. An identification problem for a linear evolution equation in a banach space. Precise estimates for biorthogonal families under asymptotic gap conditions. Global existence for Laplace reaction-diffusion equations.

Singular parabolic equations with interior degeneracy and non smooth coefficients: The Neumann case. A generalized Cox-Ingersoll-Ross equation with growing initial conditions. Mean periodic solutions of a inhomogeneous heat equation with random coefficients. The Stokes problem in fractal domains: Asymptotic behaviour of the solutions. Stability and errors analysis of two iterative schemes of fractional steps type associated to a nonlinear reaction-diffusion equation. Joint identification via deconvolution of the flux and energy relaxation kernels of the Gurtin-Pipkin model in thermodynamics with memory.

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Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators. On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms. Claudianor O. Alves , M. Cavalcanti , Valeria N. Domingos Cavalcanti , Mohammad A.

Non-autonomous attractors for integro-differential evolution equations. A new finite element scheme for Landau-Lifchitz equations. Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions. Dynamics of ratio-dependent Predator-Prey models with nonconstant harvesting. Birth of canard cycles. A simple proof of well-posedness for the free-surface incompressible Euler equations. New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws. Exact solutions of nonlinear partial differential equations.

Barbara Abraham-Shrauner. Modeling the transmission dynamics of avian influenza with saturation and psychological effect.

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## Formal Methods for Discrete-Time Dynamical Systems

More Call for special issues. Email Alert Add your name and e-mail address to receive news of forthcoming issues of this journal:. In he became a professor and in a full professor at the same university Since he has been a professor at the Bialy-stok University of Technology. In he was elected a corresponding member and in a full member of the Polish Academy of Sciences.

In he was elected an honorary member of the Hungarian Academy of Sciences. He has been granted honorary doctorates by 11 universities. His research interests cover systems theory, especially singular multidimensional systems, positive multidimensional systems, singular positive 1D and 2D systems, as well as positive fractional 1D and 2D systems.

He initiated research in the field of singular 2D, positive 2D and positive fractional linear systems.

He has published 28 books 8 in English and over scientific papers. He has also supervised 69 Ph. He is the editor-in-chief of the Bulletin of the Polish Academy of Sciences: Technical Sciences and a member of editorial boards of ten international journals. Minimum energy control of fractional descriptor positive discrete-time linear systems Academic research paper on " Mathematics ".

Similar topics of scientific paper in Mathematics , author of scholarly article — Tadeusz Kaczorek Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs. Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition. Minimum energy control of fractional positive continuous-time linear systems using Caputo-Fabrizio definition.

## On stability of discrete-time systems under nonlinear time-varying perturbations

Reachability of standard and fractional continuous-time systems with constant inputs. Sci, , Vol. Keywords: fractional system, descriptor system, positive system, minimum energy control. Introduction A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs.

The minimum energy control problem for standard linear systems was formulated and solved by Klamka ; ; and for 2D linear systems with variable coefficients by Kaczorek and Klamka Kaczorek n x n identity matrix. The following elementary row operations will be used Kaczorek, ; : 1.

Interchange of the i-th and j-th rows. This operation will be denoted by L[i, j]. Performing elementary row operations on the array [ E Aa —Ec Solution for the standard equivalent system and the positivity of fractional descriptor systems To find a solution xi of the standard discrete-time linear system 5 , we shall apply the Z-transform method.

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Theorem 2. The solution of Eqn. Therefore, the fractional descriptor system 1 with 0. The positive system 5 is reachable in n steps if and only if the reachability matrix where Rn is defined by In this case, the reachability matrix 33 has the form The matrix 35 contains three linearly independent monomial columns, and by Theorem 4 the positive fractional descriptor system is reachable in two steps. Minimum energy control problem Consider the fractional descriptor positive system 1 reduced to the form 2.

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Procedure 1. Step 1. Step 2. Using 33 , compute Rh.

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Step 3. For given Q, using 41 , compute Q Step 4. Using 40 , compute Wh and W Step 5. Step 6. Using 46 , compute the minimal value of the performance index I u. Using Procedure 1 and results of Example 3, we obtain the following. The matrix R4 is given by Note that the optimal input sequence 58 is different from the input sequences 36 and Concluding remarks Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems have been established Theorems 1 and Theorem 3.

References Buslowicz, M. Oldham, K. Podlubny, I. Received: 21 November Revised: 22 January His main field of interest is positive dynamical systems, including applications to biology and economics. He has written many books on mathematics and on economics, as well as numerous articles within these fields, including articles on algebraic number theory, opinion dynamics, decision theory, social choice.

His most recent book is Positive dynamical systems in discrete time. Theory, models, and applications , De Gruyter, Berlin, Contact Us: