First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...

This paper offers new, necessary and sufficient conditions for delay-dependent asymptotic stability of systems of the form 0 1 ( 1) ( ) ( ) x k A x k A x k h + = + − . The time-dependent criteria are derived by Lyapunov’s direct method. Two matrix equations have been derived: matrix polynomial equation and discrete Lyapunov matrix equation. Also, modifications of the existing sufficient conditi...

In this article, the backstepping control scheme is proposed to stabilize fractional order Riccati matrix differential equation with retarded arguments in which derivative presented using Caputo's definition of derivative. The results are established Mittag-Leffler stability. Lyapunov function defined at each stage and negativity an overall ensured by proper selection law. Numerical simulation ...