A new comparison theorem for scalar Riccati equations

A New Comparison Theorem for Scalar Riccati Equations

A comparison theorem for matrix Riccati difference equations

Difference equations of the form X ( t ) = F * ( t ) X ( t 1 ) F ( t ) F * ( t ) X ( t 1)G(t)[ l + G * ( t ) X ( t 1)G(t)]t G * ( t ) X ( t 1)F(t)+ Q(t ) and their associated Hermitian matrices H ( t ) = (0 v F* _C,C.)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to t...

A Quantitative Comparison Theorem for Nonlinear Equations

In the present paper we establish a quantitative comparison theorem for positive solutions of the following initial value problems 8 < : (p 1 (r)(u)ju 0 j m?2 u 0) 0 + q 1 (r)f(u) = 0 u(0) = u 0 ; u 0 (0) = 0 and 8 < : (p 2 (r)(v)jv 0 j m?2 v 0) 0 + q 2 (r)f(v) = 0 v(0) = v 0 ; v 0 (0) = 0 with r > 0 and m > 1, and also show some applications of the theorem to the non-existence problem of posit...

New Riccati equations for well-posed linear systems

We consider the classic problem of minimizing a quadratic cost functional for well-posed linear systems over the class of inputs that are square integrable and that produce a square integrable output. As is well-known, the minimum cost can be expressed in terms of a bounded nonnegative selfadjoint operator X that in the finite-dimensional case satisfies a Riccati equation. Unfortunately, the in...

New fundamental solution for time-varying differential Riccati equations

Using the tools of semiconvex duality and max-plus algebra, this work derives a new fundamental solution for the matrix differential Riccati equation (DRE) with time-varying coefficients. Such a fundamental solution, is the counterpart of the state transition matrix in linear time-varying differential equations, and can solve the DRE analytically starting with any initial condition. By parametr...