By Assoc. Prof. Dimiter Driankov, Dr.-Ing. Rainer Palm (auth.), Assoc. Prof. Dimiter Driankov, Dr.-Ing. Rainer Palm (eds.)

Model-based fuzzy regulate makes use of a given traditional or a fuzzy open loop of the plant lower than keep watch over so one can derive the set of fuzzy if-then ideas constituting the corresponding fuzzy controller. additionally, of valuable curiosity are the resultant balance, functionality, and robustness research of the ensuing closed loop approach regarding a standard version and a fuzzy controller, or a fuzzy version and a fuzzy controller. the foremost aim of the model-based fuzzy keep an eye on is to take advantage of the complete to be had variety of latest linear and nonlinear layout of such fuzzy controllers that have greater balance, functionality, and robustness homes than the corresponding non-fuzzy controllers designed by way of those comparable techniques.

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A 0 Thus, the fuzzy system (13) is asymptotically stable in the large. D. In the theorems that follow we still use the PDQ Lyapunov function (2) and the fuzzy control law (2). 2: Given a state feedback fuzzy control law (12) and the approximate upper bound in (24), if there exist constants 101 > 0, 1= 1,2, ... , m, and a set of positive-definite symmetric matrices (Qb Qz, ... , Qm) such that: (i) a set of Riccati equations [AI + BIKd T PI + PI [AI + BIKd + 101 PI PI +~(E~ + ElzKdT(E/l + ElzKd + QI 10 1 x{t) E SI, (50) = 0, 1 = 1,2, ...

15. This figure also shows the existence of two saddle points in plant C. They also limit the attraction basin of the origin. Finally, the qualitative behavior of plant D is a combination on the behaviors of plants Band C. The changes between the state portraits shown in the left column of Fig. 15 are due to the occurrence of the bifurcations mentioned in the introduction. First consider the pitchfork bifurcation at infinity Poo • This bifurcation happens at the transition between plants A and C, or between plants Band D.

If the accurate upper bounds can be found, the stability condition (37) or (38) becomes a necessary condition. 2 we can deduce that the positive-definite solutions decrease monotonically as CI -+ O. Therefore, we can propose the following stability checking algorithm. The stability checking algorithm: Step 1. Suppose that the upper bounds (24) are given and set 1, 2, ... , m to a set of positive values, for example, CI = 1, CI, I = in = m. Step 2. Determine whether the set of Riccati equations (37) or (38) has a set of positive-definite symmetric solutions.