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We provide a less conservative (compared with our previous results) lower bound on the horizon length for a stabilizing model predictive control algorithm where the terminal cost is not assumed to be a local control Lyapunov function. Our main additional assumption is that the value function is bounded by a linear function of a measure of the state(More)
In this paper we introduce homogeneity for hybrid systems (using generalized dilations) and provide basic implications of this property similar to that of continuous-time and discrete-time homogeneous systems. In our main result we state that stability of a hybrid system that is robust with respect to small perturbations implies the existence of a(More)
Feedback-based treatment scheduling for HIV patients is summarized. The feedback schedules are developed using a dynamic HIV infection model that has appeared in the literature. The theory behind the feedback schedules is nonlinear model predictive control. This branch of nonlinear control theory is reviewed, limitations are pointed out, and recent(More)
We consider discrete-time homogeneous control systems that undergo arbitrary switching. We propose an optimization-based, constructive method (which can be numerically realized) to generate a homogeneous control Lyapunov function and a homogeneous feedback law that stabilizes the origin for all possible switching scenarios. The established stability is(More)
We introduce generalized dilations, a broader class of operators than that of dilations, and consider homogeneity with respect to this new class of dilations. For discrete-time systems that are asymptotically controllable and homogeneous (with degree zero) we propose a method to numerically approximate any homogeneous value function (solution to an infinite(More)
In this paper, we consider homogeneity (of discrete-time systems) with respect to generalized dilations, which define a broader class of operators than dilations. The notion of generalized dilations allows us to deal with the stability of attractors that are more general than a single point, which may be unbounded sets. We study homogeneous difference(More)
We present robust stability results for discrete-time nonlinear systems using certainty equivalence output feedback, particularly those that employ a model predictive control (MPC) formulation to generate the feedback control law. To this end, we discuss nominal robustness properties of general discrete-time nonlinear systems, including those that use(More)
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