1,720,986 research outputs found
A remark on Ryan's generalization of Brockett's condition to discontinuous stabilizability
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Finite valued feedback laws and piecewise classical solutions
No full textOften, in engineering literature, we find control systems in which the open loop inputs are piecewise constant and take values in a finite set. Such open loop inputs cause the system to have fairly regular solutions. On the other hand, when acting in closed loop, feedback laws taking values in a finite set may not be reinterpreted as open loop inputs of the considered type. In fact, pathological behaviours such as the accumulation of discontinuities may appear (Zeno phenomenon). We give some conditions which can be used as tools for building finite valued feedback laws not causing such pathological behaviour
Discrete Valued Feedback Laws and Zeno Phenomenon
No full textWe consider closed loop control systems in which feedback laws take values in a discrete set U and we study the Zeno phenomenon, i.e. the accumulation of discontinuities with respect to time. The results generalize those obtained in [F. Ceragioli, Finite valued feedback laws and piecewise classical solutions, Nonlinear Analysis 65 (2006) 984-998] for the case where U is finite to the case where U may be infinite. An application to a quantized control problem is also show
Finite L-2-gain with Nondifferentiable Storage Functions
No full textWe consider affine control systems with the finite L2-gain property in the case the storage function is not differentiable. We generalize some classical results concerning the connection of the finite L2-gain property with the stability property of the unforced system, the characterization of the infinite L2-gain by means of partial differential inequalities of the Hamilton-Jacobi type and the problem of givin to a system the finite L2-gain property by means of a feedback law. Moreover, we introduce and study the apparently new notion of exact storage functio
Nonpathological Lyapunov functions and discontinuous Caratheodory systems
No full textDifferential equations with discontinuous righthand side and solutions intended in Carath\'eodory sense are considered. For these equations, sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also prove
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