The Perturbation Estimates Of The Solution To The Discrete Riccati Matrix Equations

Discrete Riccati matrix algebra equation plays a key role in the analy-sis、comprehensiveness and design in linear quadratic gaussian control systemand linear optimal fltering system. In optimal control feld, many problemsreduce to discussing solving the solution and the solution properties of therelative discrete Riccati matrix equation. In recent years, many scholars athome and abroad pay much attention to the solution and its perturbation ofthis matrix equation, and they have gotten a lot of results.In the passage, we frstly give some upper and lower bounds of the solu-tion for the discrete Riccati matrix equation. Further, we discuss the pertur-bation problem of this equation.The paper is constructed with three chapters:In chapter one, we introduce the background and the research status ofthe discrete Riccati matrix equation. Meanwhile, we give some fundamentaluseful symbols and defnitions.In chapter two, by using classical eigenvalue inequality, combining themethod to solving one variable quadratic inequality with some inequality tech-niques, we obtain some upper and lower bounds of the solution for the discreteRiccati matrix equation.In chapter three, if the discrete Riccati matrix equation and its pertur-bation equation exist positive defnite solutions, we discuss the perturbationbounds of the positive defnite solution by applying the derived upper andlower bounds in chapter two, combining with the properties of inverse matrixand matrix norm. Meanwhile, we give numerical examples to illustrate theefectiveness.