On Eigenvalue Bounds Of The Discrete Algebraic Riccati Equations And The Discrete Coupled Algebraic Riccati Equation

Riccati equations are widely applied to various engineering areas, for example, inthe area of control system stability analysis, optimal and robust controllers, etc. Thus,lots of scholars pay much attention to the discrete algebraic Riccati equations and itscoupled equations, meanwhile they have obtained plenty of achievements.If those equations exist unique symmetric positive definite solutions, we improvethe bounds about the eigenvalues, certain sums and products of the eigenvalues for thesolutions.Main contents as follows:In chapter one, we introduce the background and the recent works for the discretealgebraic Riccati equations, then we showed the main work and some symbols whichwill be used in our paper.In chapter two, we obtain the bounds about the eigenvalues for the unique symmet-ric positive definite solutions by using inequality theory and the nature of the symmetricpositive definite solutions for the Riccati matrix equations. Moreover by combining thederived results with the inequality theory, we obtain certain sums or products of theeigenvalues for the solutions. Examples explain the efectiveness.In chapter three, on the basis of the recent references, combining the monotonicityof the function with the properties of concave function, we obtain the upper boundsabout the solutions and its’ eigenvalues. Examples explain the efectiveness.