This paper presents an indirect adaptive control scheme of continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the ...

In this paper, based on the inner-outer (IO) iteration framework [17], by introducing some tunable parameters, an SOR-type IO (SIO) method is proposed for solving Sylvester matrix equation and coupled Lyapunov equations (CLMEs) in discrete-time jump linear systems with Markovian transitions. Fisrtly, SIO algorithm discrete developed, its convergence property analyzed choices of parameters are a...

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

This paper deals with the model reference tracking control problem of linear systems based on observer for Markov jump unknown transition rates. The main contributions are as follows: Firstly, we designed a descriptor given by matrix transformation. Then, law composed feedforward compensator and feedback was calculating variations observer. part can stabilize system. is complete parametric comp...

Based on the well-known Leverrier algorithm, a simple explicit solution to right factofization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equations and the problem of parametric eigenstructure assignment by state feedback a...

This is a collection of classical results about resultants and discriminants for polynomials, compiled mainly for my own use. All results are well-known 19th century mathematics, but I have not investigated the history, and no references are given. 1. Resultant Definition 1.1. Let f(x) = anx n + · · ·+ a0 and g(x) = bmx + · · ·+ b0 be two polynomials of degrees (at most) n and m, respectively, ...

‎In this paper‎, ‎an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed‎. ‎The convergence analysis of the algorithm is investigated‎. ‎We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions‎. ‎Finally‎, ‎some numerical examples are given to demons...