In this paper, we consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. For continuous-time switched linear systems, we show that if there exists a common positive definite matrix f...

The control of discrete systems with time-varying delays has been researched extensively in the last few decades. Especially in recent years there are increasing interests in discrete-time systems with delays due to the emerging fields of networked control and network congestion control (Altman & Basar 1999; Sichitiu et al., 2003; Boukas & Liu 2001). Stability problem for linear discrete-time s...

Abstract This work studies receding-horizon control of discrete-time switched linear systems subject to polytopic constraints for the continuous states and inputs. The objective is approximate optimal strategy cases in which online computation intractable due necessity solving mixed-integer quadratic programs each discrete time instant. proposed approach builds upon an approximated finite-horiz...

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate l...

This paper presents necessary and sufficient conditions for quadratic stability and stabilization of uncertain linear discrete systems with state delay. The system under consideration involves state time delay and time-varying norm-bounded parameter uncertainties appearing in all the matrices of the state-space model. The results are obtained in terms of linear matrix inequality. A robustly sta...

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic quadratic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are...

A method is proposed for reducing the cost of computing search directions in an interior point method for a quadratic program. The KKT system is partitioned and modified, based on the ratios of the slack variables and dual variables associated with the inequality constraints, to produce a smaller, approximate linear system. Analytical and numerical results are included that suggest the distribu...

Efficient Riccati equation based techniques for the approximate solution of discrete time linear regulator problems are restricted in their application to problems with quadratic terminal payoffs. Where non-quadratic terminal payoffs are required, these techniques fail due to the attendant nonquadratic value functions involved. In order to compute these non-quadratic value functions, it is ofte...