Essentials of nonlinear control theory by James R. Leigh

By James R. Leigh

The booklet is anxious with realizing the constitution of nonlinear dynamic structures inside a regulate engineering context After a dialogue of theoretical foundations, the improvement strikes to precise concepts (describing functionality approach, part airplane portrait, linearisation methods). The therapy then turns into orientated to qualitative research and continues this emphasis to the tip of the publication. The vast goal is to increase equipment that may let the topology of method behaviour to be visualised. the most instruments are Lyapunov tools, extending to incorporate fresh paintings on process decomposition. A bibliography lists either prior seminal and up to date literature to permit the reader to keep on with up specific facets

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12. By informed guesswork, the figure can be extended to give estimates of behaviour in other regions of the phase plane. Some guidelines are: (a) Trajectories cannot cross except at critical points. (b) The behaviour of a system with continuous equations will undergo a smooth transition from the locally linear behaviour around critical points. In particular the eigenvector directions, straight over the whole phase plane for a linear system, can be expected to curve as they move away from their critical point.

1 may aid visualisation of the above concepts. V=k Fig. 5 Determination of the extent of a region of asymptotic stability around the origin In those cases where a system has a finite region U that is asymptotically stable to the origin it will usually be the aim of Lyapunov analysis to discover, at least approximately, the extent of the region £/. Moving outwards into phase space from the origin, the limit of asymptotic stability may be set by V failing to remain negative definite. 7). 6 The search for a Lyapunov function A major disadvantage in Lyapunov's direct method is that stability is assured 'if there exists a Lyapunov function'.

Fig. 1 may aid visualisation of the above concepts. V=k Fig. 5 Determination of the extent of a region of asymptotic stability around the origin In those cases where a system has a finite region U that is asymptotically stable to the origin it will usually be the aim of Lyapunov analysis to discover, at least approximately, the extent of the region £/. Moving outwards into phase space from the origin, the limit of asymptotic stability may be set by V failing to remain negative definite. 7). 6 The search for a Lyapunov function A major disadvantage in Lyapunov's direct method is that stability is assured 'if there exists a Lyapunov function'.

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