A note on stable matrices

A Note on Families of Stable Matrices

Many topological properties of the whole family of stable polynomials and matrices have been studied in a number of publications (see e.g., [1,3–7,11,12]). The present paper continues these investigations with the aim of strengthening these results in the sense that instead of simple-connectivity we show stronger property of contractibility of the various families of stable matrices from this p...

Ela a Note on Simultaneous Block Diagonally Stable Matrices

Abstract. Consider a set of square real matrices of the same size A = {A1, A2, . . . , AN}, where each matrix is partitioned, in the same way, into blocks such that the diagonal ones are square matrices. Under the assumption that the diagonal blocks in the same position have a common Lyapunov solution, sufficient conditions for the existence of a common Lyapunov solution with block diagonal str...

A note on simultaneous block diagonally stable matrices

A note on positive deniteness and stability of interval matrices

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

A note on positive deniteness and stability of interval matrices

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...