This paper presents a general framework for analyzing stability of nonlinear switched systems, by combining the method of multiple Lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures. For deterministic switched systems, this leads to a unification of representative existing results and an… (More)
Stochastic receding horizon control with output feedback and bounded controls. HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.… (More)
Probabilistic Computation Tree Logic (PCTL) is a well-known modal logic which has become a standard for expressing temporal properties of finite-state Markov chains in the context of automated model checking. In this paper, we consider PCTL for noncountable-space Markov chains, and we show that there is a substantial affinity between certain of its… (More)
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then reformu-lated in terms of probabilistic constraints. It is shown that, for a suitable parametrization of the control… (More)
We propose a method of stability analysis of switched systems perturbed by a Wiener process. Our result utilizes the method of multiple Lyapunov functions, and is analogous to an existing result for deterministic switched systems.
This thesis presents a study on stability analysis and stabilizing controller synthesis of randomly switched systems. These systems have two ingredients: a family of nonlinear subsystems and a random switching signal that specifies which subsystem is active at each time instant. In broad strokes, the approach pursued here consists of identifying key… (More)
We present sufficient conditions for almost sure global asymptotic stability (gas a.s.) of randomly switched systems via multiple Lyapunov-like functions. For systems possessing control inputs we present a method for designing controllers which render the closed-loop randomly switched system gas a.s.
In this paper we prove that a switched nonlinear system has several useful input-to-state stable (ISS)-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching… (More)
This paper describes the swing-up and stabilization of a cart–pendulum system with a restricted cart track length and restricted control force using generalized energy control methods. Starting from a pendant position, the pendulum is swung up to the upright unstable equilibrium conÿguration using energy control principles. An " energy well " is built… (More)