In the paper, we consider interval linear algebraic systems of equations Ax = b, with an interval matrix A and interval right-hand side vector b, as a model of imprecise systems of linear algebraic equations of the same form. We propose a new regularization procedure that reduces the solution of the imprecise linear system to computing a point from the tolerable solution set for the interval li...

For a given standard Hamiltonian H with arbitrary complex scalar and vector potentials in one-dimension, we construct an invertible antilinear operator τ such that H is τ -anti-pseudo-Hermitian, i.e., H = τHτ−1. We use this result to give the explicit form of a linear Hermitian invertible operator with respect to which any standard PT symmetric Hamiltonian with a real degree of freedom is pseud...

System identification is very important to technical and nontechnical areas. All physical systems are nonlinear to some extent and it is natural better to use nonlinear model to describe a real system. The Wiener and Hammerstein systems are proved to be good descriptions of nonlinear dynamic systems in which the nonlinear static subsystems and linear dynamic subsystems are separated in differen...

The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuousand discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized sy...

In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear systems and have found applications in the analysis of nonlinear systems. On the other hand, there is n...

2 mation is actually a rational model with a time delay. Through illustrations, we show that the pseudo-rational approximation is simple and effective. It commensurate form. Useful MATLAB codes are also included in the appendix.

The paper considers pseudo-differential boundary value control systems. The underlying operators form an algebra D with the help of which we are able to formulate typical boundary value control problems. The symbolic calculus gives tools to form e.g. compositions, formal adjoints, generalized right or left inverses and compatibility conditions. By a parametrizability we mean that for a given co...