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Further Results on the Control Law via the Convex Hull of Ellipsoids
  • Nguyen Hoai Nam
Nguyen Hoai Nam

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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.