摘要:This research work considers the problem of scalar and matrix solution bounds derivation for one class of parameter dependent Lyapunov equations (PDLEs). It is assumed, that the coefficient matrix is a matrix polytope, where the uncertain vector is defined on the unit simplex. It is shown that this problem can be efficiently solved by making use of some previously obtained results, concerning the exact conditions for positive definiteness of homogeneous matrix polynomials (HMPs). The main contribution consists in the definition of two upper bounds − for the trace and the maximum eigenvalue of the solution of a PDLE. The applicability of these results is illustrated by a numerical example.