Dynamical systems with saturation nonlinearities: analysis and design
The book is more on the circuit theory, esp. the neural network theory than on the control or systems theory. The senior author was the editor of IEEE Transactions on Circuits and Systems. Some basic results are as follows. For a class of linear continuous-time dynamical system with saturation the null solution will be globally asymptotically stable if some measure of the state matrix is negative. For discrete-time systems are constructed two Lyapunov functions. For a discrete-time system with saturation are given the conditions under which it can be stabilized by constrained controllers. The least restrictive criterion for testing limit cycles in fixed-point digital filters is given. Several sufficient conditions for the global asymptotic stability of zero state equilibrium of 2-D digital filters subject to overflow nonlinearities are established. For quadratic forms are presented necessary and sufficient criteria for the construction of Lyapunov functions. The next are considered neural networks which have the structure of analog Hopfield neural networks. All equilibria are then located and their stability determined. The synthesis procedure for associative memories which guarantee to store the desired patterns. Synthesis procedure for artificial neural networks with prespecified interconnection structure is presented.
scientific article; zbMATH DE number 626634