In this paper we study the quadratic regulator problem for a process governed by a Volterra integral equation in IR. Our main goal is the proof that it is possible to associate a Riccati differential equation to this quadratic control problem, which leads to the feedback form of the optimal control. This is in contrast with previous papers on the subject, which confine themselves to study the F...

In this paper, new oscillation conditions for the 2nd-order noncanonical neutral differential equation (a0t((ut+a1tug0t)′)β)′+a2tuβg1t=0, where t≥t0, are established. Using Riccati substitution and comparison with an of first-order, we obtain criteria that ensure studied equation. Furthermore, complement improve previous results in literature.

A new fundamental solution semigroup for operator differential Riccati equationsis developed. This fundamental solution semigroup is constructed via an auxiliary finite horizonoptimal control problem whose value functional growth with respect to time horizon is determinedby a particular solution of the operator differential Riccati equation of interest. By exploiting semi-convex...

In this paper, we consider the hermitian Riccati difference equations. Analogous to a differential equation, there is connection between equation and its associated linear equation. Based on can obtain an explicit representation for solution of define extended solution. Further, characterize asymptotic state rate convergence. Constant equilibrium solutions, periodic solutions closed limit cycle...

In this paper, by constructing the equivalent form of the continuous algebraic Riccati equation (CARE) and applying some matrix inequalities, a new lower bounds solution of the CARE is proposed. Finally, corresponding numerical examples are provided to illustrate the effectiveness of the results.

In this paper, two di erent approaches to the H1 control by state feedback are related and discussed. The rst approach is based on the solvability of an algebraic Riccati equation and the second one explores the convexity of the set de ned by a matrix inequality. New insights are provided in order to establish the relationship between the set of stabilizing gains obtained from the two di erent ...

Abstruct-The determination of the state-space equations of a time-varying finite-dimensional linear system with a prescribed output covariance matrix is considered when the system is excited by Gaussian whitenoise inputs. It is shown that a symmetric state covariance matrix provides the key link between the statespace equations of a system and the system output covariance matrix. Furthermore, s...

In this paper we study the algebraic Riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system. The construction of the controller involves solving the full-order algebraic Riccati equation with small parameter ε. Under control-oriented assumptions, we first provide the sufficient conditions such that the full-order algebraic Riccati equat...

Upper bounds for eigenvalues of a solution to continuous time coupled algebraic Riccati equation (CCARE) and discrete time coupled algebraic Riccati equation (DCARE) are developed as special cases of bounds for the uni...ed coupled algebraic Riccati equation (UCARE). They include bounds of the maximal eigenvalues, the sums of the eigenvalues and the trace.

This paper suggests a closed-form solution of particular case of an algebraic Riccati equation and its application example to optimal and smooth motion planning for a given linear quadratic performance index. Actually, the algebraic Riccati equation can be changed into Moser-Veselov equation by deriving both symmetric and skew-symmetric conditions from an algebraic Riccati equation itself. Also...