A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...

For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solution P(t,x). Then the closed-loop optimal strategies are given by u(t) = −R−1B∗P(t,x(t)), v(t) = −S−1C∗P(t,x(t)). For differential game problems of...

A stochastic linear quadratic (LQ) control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite. Indefinite stochastic LQ theory has been extensively developed and has found interesting applications in finance. However, there remains an outstanding open problem, which is to identify an appropriate Riccati-type equation whose solvabili...

This work addresses the problems of robust exponential stability and stabilization for uncertain linear non-autonomous control systems with discrete and distributed time-varying delays and nonlinear perturbations. Based on the combination of the Riccati differential equation approach and the Lyapunov-Krasovskii functional, new sufficient conditions are derived in terms of the solution of Riccat...

Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei–Norman method is applied for obtaining the associated differential equation in the group SL(2,R). The superposition principle for first order differential equation systems and Lie-Scheffers theorem are also analysed f...

In this work, some new interval oscillation criteria for solutions of a class of nonlinear fractional differential equations are established by using a generalized Riccati function and inequality technique. For illustrating the validity of the established results, we also present some applications for them. Key–Words: Oscillation; Interval criteria; Qualitative properties; Fractional differenti...