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By Jean-Jacques Slotine, Weiping Li

ISBN-10: 0130408905

ISBN-13: 9780130408907

Covers in a innovative style a few research instruments and layout suggestions without delay acceptable to nonlinear keep an eye on difficulties in excessive functionality platforms (in aerospace, robotics and car areas).

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6. The vertical axis represents . I s\vitching line, because the control input and thus the phase trajectories are switched on that line. It is interesting motions to see that, starting from a nonzero initial angle. rilldic Sect. 2 Cortstructing Phase Portraits 27 under the action of the jets. 1. 3). THE METHOD OF ISOCLINES The basic idea in this method is that of isoclines. 1). 5). An isocline is defined to be the locus of the points with a given tangent slope. An isocline with slope a is thus defined to be This is to say that points on the curve all have the same tangent slope a.

Extensions of the concepts and results to non-autonomous systems will be studied in chapter 4. EQUILIBRIUM POINTS It is possible for a system trajectory to correspond to only a single point. Such a point is called an equilibrium point. As we shall see later, many stability problems are naturally formulated with respect to equilibrium points. 44 Fundamentals of Lyapunov Theory Chap. 2 A state x* is an equilibrium state (or equilibrium point; 01. the system if once x(t) is equal to x*, it remains equal to x* for all future time.

Third, it can deal with the "hard nonlinearities" frequently found in control systems ,without any difficulty. As a result, it is an important tool for practical problems of nonlinear control analysis and design. :tions (false predictions may be made if certain conditions are not satisfied) and restrii:tions on the systems to which it applies (for example, it has difficulties in dealing with systems with multiple nonlinearities). Chapter 2 Phase Plane Analysis Phase plane analysis is a graphical method for studying second-order systems.

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Applied Nonlinear Control by Jean-Jacques Slotine, Weiping Li


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