The convex hull of ellipsoids was suggested in the literature for robust invariance of constrained uncertain and/or time-varying linear discrete-time systems. It was show that a robust invariant set obtained with the convex hull of ellipsoids can be significantly larger than that with the ellipsoidal set. However, the design conditions are given in terms of bilinear matrix inequalities (BMIs), which are non-convex. The main purpose of this paper is to present a way to overcome this weakness by providing new convex linear matrix inequality (LMI) design conditions. It is shown that the conditions are losslessly extended to robust controlled invariance and to nonlinear state feedback control design. Two examples are included with comparison to earlier solutions from the literature to illustrate the results.

A new Lyapunov function based on the convex hull of ellipsoids was introduced in [7] for the study of uncertain and/or time-varying linear discrete-time systems with/without constraints. The new Lyapunov function has many attractive features such as: i) it provides a necessary and sufficient conditions for robust stability and robust stabilization; ii) the design conditions are formulated as linear matrix inequality constraints. The control law is obtained by solving a convex optimization problem online. This optimization problem generally does not have a closed-form solution, and hence it is solved by numerical methods. In this paper, we intend to complement the results in [7] by analyzing the geometric structures of the solution of the optimization problem, and of the control law. In particular, we show that the control law is a piecewise linear and continuous function of the state.

The objectives of this paper are twofold. The first is to present a particular choice of the parameters of dynamic feedback laws for polytopic uncertain and/or time-varying systems with state and input constraints. We show that it has the same desired property as that of algorithms in [1], [2], i.e., the domain of attraction of the controlled system under a linear/saturated dynamic feedback law is identical to the domain of attraction under any static linear/saturated state feedback law. The second objective is to propose new procedures for robust constrained prediction dynamics based MPC that do not require the assumption of quadratic stability. With respect to other well known techniques, the main advantages of this new approach is the reduced conservativeness.

There exist several approaches to design the optimal control strategy to harvest wave energy with a point absorber. However they are generally based on the assumption that the WEC and the PTO dynamics are well-known. In the practical WEC control implementation, this is generally not the case. The objective of this paper is to design a robust optimal control strategy that can take into account the uncertain WEC and PTO dynamics. Our choice is a robust adaptive PI control law. The proposed controller is validated and compared through simulation for irregular sea states.

This paper provides a solution for a linear command governor (CG) that employs invariant and constraint-admissible ellipsoid. The motivation is to substitute the typical polyhedral set used in almost all CG schemes with the ellipsoidal one, which is much easier to construct. However the price for this offline computational efficiency is that the size of the feasible set can be relatively small, and the online computational burden is heavier than that of polyhedral set based CGs. The proposed solution overcomes these two weaknesses and offers a very attractive alternative to polyhedral set based CG. Two numerical examples with comparison to earlier solutions from the literature illustrate the effectiveness of the proposed algorithm.

In this paper, we propose a new technique for the performance analysis of discrete-time linear systems controlled by a saturated linear control law. Two performance indices, the computation of invariant sets and the L2 performance, are considered. The main contributions of the paper are the following: i) a new linear parameter varying system framework is presented to model the saturated system, ii) a nonlinear saturation-dependent auxiliary feedback matrix is considered, iii) new sufficient conditions for the performance analysis are proposed. It is shown that the conditions can be expressed as a set of linear matrix inequalities. Furthermore, it is shown that the conditions are guaranteed to be less conservative than existing solutions in the literature. Three numerical examples are presented to illustrate the effectiveness of the proposed method.