The main feature of a Takagi-Sugeno (T-S) fuzzy model is to express the local dynamics of each fuzzy implication (rule) by a linear system model. The overall fuzzy model of the system is achieved by fuzzy “blending” of the linear system models. Parallel or feedback connections of T-S fuzzy systems which preserve the properties of each system are possible [1]. Thus a simple and straightforward a...

Takagi–Sugeno (T–S) fuzzy models play an important role in nonlinear control because they can be used to approximate nonlinear systems. Also, for the affine T–S fuzzy models, the local linear sub-system properties can be easily related to the physics of the controlled nonlinear system. This is one advantage of the affine T–S fuzzy models relative to the homogeneous T–S fuzzy models. In the lite...

Finite affine groups are given by groups of translations and di- lations on finite cyclic groups. For cyclic groups of prime order we develop a time-scale (wavelet) analysis and show that for a large class of non-zero window signals/vectors, the generated full cyclic wavelet system constitutes a frame whose canonical dual is a cyclic wavelet frame.

We investigate necessary and sufficient conditions under which a nonlinear affine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given affine connection, and on the input-output behavior of the prolonged system...

A singular control system SG on G is defined by a pair E, D of.type for a single-input, control affine, nonlinear system in small dimension. Has on the optimality of singular controls when the control is replaced with.ABSTRACT A normal form for open loop control systems is provided, based on their interpretation as skew product flows and on normal forms for.Introduction. In this paper, the foll...

finite affine groups are given by groups of translations and di-lations on finite cyclic groups. for cyclic groups of prime orderwe develop a time-scale (wavelet) analysis and show that for alarge class of non-zero window signals/vectors, the generatedfull cyclic wavelet system constitutes a frame whose canonicaldual is a cyclic wavelet frame.

Abstract. We investigate necessary and sufficient conditions under which a general nonlinear affine control system with outputs can be written as a gradient control system corresponding to some pseudoRiemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the systemwith respect to a given affine connection, and on the output behavior of the prolon...

Sufficient conditions under which a class of nonlinear discrete-time systems which are non-affine in the control input and the states can be rendered locally dissipative are derived. Two methodologies in order to render nonlinear single-input single-output discrete-time systems locally dissipative are given. Dissipativity is seen as a “perturbation” of the storage energy invariance or the feedb...

In this paper, we propose an observer-based fuzzy adaptive control scheme for a class of multiple-input-multiple-output (MIMO) nonlinear non-affine systems with uncertainty and unknown state derivative. The proposed approach combines the recurrent-type fuzzy logic system (RFLS) and nonlinear observer to deal with the tracking control problem. It adopts the RFLS to approximate nonlinear unknown ...