First order algebraic differential equations are considered. An necessary condition for a first order algebraic differential equation to have a rational general solution is given: the algebraic genus of the equation should be zero. Combining with Fuchs’ conditions for algebraic differential equations without movable critical point, an algorithm is given for the computation of rational general s...

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...

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure ...

A class of hyperbolic distributed parameter time-varying system on the interval [0,∞) is considered. The corresponding linear-quadratic (LQ) optimal control problem is studied by using the infinite-dimensional state-space formulation and the well-known Riccati equation approach.

This paper is concerned with the problem of H m estimation for linear discrete-time systems with timevarying norm-bounded parameter uncertainty in both the state and output matrices. We design an estimator such that the estimation error dynamics is quadratically stable and the induced operator norm of the mapping from noise to estimation error is kept within a prescribed bound for all admissibl...

Numerically reliable algorithms to compute the periodic non-negative definite stabilizing solutions of the periodic differential Riccati equation (PRDE) and discrete-time periodic Riccati equation (DPRE) are proposed. For the numerical solution of PRDEs, a new multiple shooting-type algorithm is developed to compute the periodic solutions in an arbitrary number of time moments within one period...

Local and non local perturbation bounds for real continuous time coupled algebraic matrix Riccati equations are deriv ed using the technique of Ly apunov majorants and xed point principles Equations of this type arise in the robust analysis and design of linear control systems

In this paper, the numerical algorithm for solving the state and output feedback H∞-constrained LQG control problem is investigated. Although the equations that have to be solved to design the controller consist of the nonlinear crosscoupled algebraic Riccati equations (CAREs), it is newly proven that both the uniqueness and the positive semidefiniteness of the iterative solutions can be guaran...

In this paper an infinite-dimensional LQR control-based design for a system containing linear hyperbolic partial differential equations coupled with linear ordinary differential equations is presented. The design is based on an infinite-dimensional Hilbert state-space representation of the coupled system. The feedback control gain is obtained by solving algebraic and differential matrix Riccati...