Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case

Stabilization via generalized homogeneous approximations

We introduce a notion of generalized homogeneous approximation at the origin and at infinity which extends the classical notions and captures a large class of nonlinear systems, including (lower and upper) triangular systems. Exploiting this extension and although this extension does not preserve the basic properties of the classical notion, we give basic results concerning stabilization and robustness of nonlinear systems, by designing a homogeneous (in the generalized sense) feedback controller which globally asymptotically stabilizes a chain of power integrators and makes it the dominant part at infinity and at the origin (in the generalized sense) of the dynamics. Stability against nonlinear perturbation follows from domination arguments

Global topological control for synchronized dynamics on networks

A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act on the topology of the inter-nodes contacts to achieve the desired degree of stabilization, without altering the dynamical parameters of the model. Both symmetric and asymmetric couplings are considered. In this latter setting the web of contacts is assumed to be balanced, for the homogeneous equilibrium to exist. The performance of the proposed method are assessed, assuming the Complex Ginzburg-Landau equation as a reference model. In this case, the implemented control allows one to stabilize the synchronous limit cycle, hence time-dependent, uniform solution. A system of coupled real Ginzburg-Landau equations is also investigated to obtain the topological stabilization of a homogeneous and constant fixed point

Pattern stabilization through parameter alternation in a nonlinear optical system

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment. The nonlinear analysis provides an explanation of the patterning under alternation and accurately predicts both the observed dependence of the patterning on the frequency of alternation, and the measured spatial frequencies of the patterns.Comment: 12 pages, 5 figures. To appear in PR

Semiglobal leader-following consensus for generalized homogenous agents

In the present paper, the Leader-Following consensus problem is investigated and sufficient conditions are given for the solvability of the problem, assuming that the agents are described by a nonlinear dynamics incrementally homogeneous in the upper bound