Linear dynamically varying H∞ controllers are developed for tracking natural trajectories of a broad class of nonlinear systems defined over compact sets. It is shown that the existence of a suboptimal H∞ controller is related to the existence of a bounded solution to a functional algebraic Riccati equation. Even though nonlinear systems running over compact sets could exhibit sensitive depende...

We investigate here the numerical solution of a special type of descriptor continuous-time Riccati equation which is involved in solving several key problems in robust control, formulated under very general hypotheses. We also give necessary and sufficient existence conditions together with computable formulas for both stabilizing and antistabilizing solutions in terms of the associated matrix ...

The low-and-high gain design technique, which was initiated in 10] for a chain of integrators and completed in 13] for general linear asymptotically null controllable with bounded controls systems, was conceived for semi-global control problems beyond stabilization and was related to the performance issues such as semi-global stabilization with enhanced utilization of the available control capa...

In this note we report on a new kind of algebraic Ric-cati equation which we encountered when studying an H 1 type problem of disturbance attenuation for stochastic linear systems. The same equation occurs in the analysis of stability radii of linear systems with both deterministic and stochastic uncertainties. The associated linear matrix inequality is also considered.

An error occurs in a part of the statement and proof Proposition 2.2 paper “Stochastic explosion non-uniqueness for α-Riccati equation” [J. Math. Anal. Appl. 476 (2019) 53–85] that is corrected this erratum. The revised result reveals new unexpected critical phenomena, having further implications solutions to nonlinear differential equation Riccati type.

By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

Normwise backward errors and residual bounds for an approximate Hermitian positive semidefinite solution set to the periodic discrete-time algebraic Riccati equation are obtained. The results are illustrated by using simple numerical examples.

Let H and Y be separable Hilbert spaces, U finite dimensional. Let A ∈ L(H), B ∈ L(U, H), C ∈ L(H,Y ), D ∈ L(U,Y ), and suppose that the open loop transfer function D(z) := D + zC(I − zA)B ∈ H∞(U, Y ). Let J ≥ 0 be a cost operator. We study a subset of self adjoint solutions P of the discrete time algebraic Riccati equation (DARE)

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, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to es...