   Oscillatority of Nonlinear Systems with Static FeedbackEfimov, Denis  ; in SIAM Journal on Control & Optimization (2009), 48(2), 618-640 New Lyapunov-like conditions for oscillatority of dynamical systems in the sense of Yakubovich are proposed. Unlike previous results these conditions are applicable to nonlinear systems and allow for ... [more ▼] New Lyapunov-like conditions for oscillatority of dynamical systems in the sense of Yakubovich are proposed. Unlike previous results these conditions are applicable to nonlinear systems and allow for consideration of nonperiodic, e.g., chaotic modes. Upper and lower bounds for oscillations amplitude are obtained. The relation between the oscillatority bounds and excitability indices for the systems with the input are established. Control design procedure providing nonlinear systems with oscillatority property is proposed. Examples illustrating proposed results for Van der Pol system, Lorenz system, and Hindmarsh–Rose neuron model as well as computer simulation results are given. [less ▲] Detailed reference viewed: 27 (1 ULg)Consensus optimization on manifoldsSarlette, Alain ; Sepulchre, Rodolphe in SIAM Journal on Control & Optimization (2009), 48(1), 56-76 The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their ... [more ▼] The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO(n) and the Grassmann manifold Grass(p,n) are treated as original examples. A link is also drawn with the many existing results on the circle. [less ▲] Detailed reference viewed: 48 (8 ULg)Stability of perturbed functional differential equations and stabilization of nonlinear cascades; Sepulchre, Rodolphe ; in SIAM Journal on Control & Optimization (2001), 40 In this paper the effect of bounded input perturbation on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global ... [more ▼] In this paper the effect of bounded input perturbation on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability in preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. This results in a general framework, in which the stabilization of partial linear cascade systems using partial state feedback can be treated systematically. [less ▲] Detailed reference viewed: 10 (1 ULg)Boundedness properties for time-varying nonlinear systems; ; Sepulchre, Rodolphe in SIAM Journal on Control & Optimization (2000), 39(5), 1408-1422 Detailed reference viewed: 6 (1 ULg) |
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