Solution methods of plants location dynamic problems in continuous-time

Global stability analysis for complex-valued artificial recurrent neural networks seems to be one of yet-unchallenged topics in information science. This chapter presents global stability conditions for discrete-time and continuous- time complex-valued recurrent neural networks, which are regarded as nonlinear dynamical systems. Global asymptotic stability conditions for these networks are derived by way of suitable choices of activation functions. According to these stability conditions, there are classes of discrete-time and continuous-time complex-valued recurrent neural networks whose equilibrium point is globally asymptotically stable. Furthermore, the conditions are shown to be successfully applicable to solving convex programming problems, for which real field solution methods are generally tedious.

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On the square-root method for continuous-time algebraic Riccati equations

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000010547 ◽

1999 ◽

Vol 40 (4) ◽

pp. 459-468 ◽

Cited By ~ 2

Author(s):

Linzhang Lu ◽

C. E. M. Pearce

Keyword(s):

Riccati Equation ◽

Continuous Time ◽

Riccati Equations ◽

Algebraic Riccati Equation ◽

Square Root ◽

Numerical Examples ◽

Algebraic Riccati Equations ◽

Solution Methods ◽

Square Root Method

AbstractWe give a simple and transparent proof for the square-root method of solving the continuous-time algebraic Riccati equation. We examine some benefits of combining the square-root method with other solution methods. The iterative square-root method is also discussed. Finally, paradigm numerical examples are given to compare the square-root method with the Schur method.

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Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

Journal of Applied Probability ◽

10.1017/s0021900200002965 ◽

2007 ◽

Vol 44 (02) ◽

pp. 285-294 ◽

Cited By ~ 2

Author(s):

Qihe Tang

Keyword(s):

Asymptotic Formula ◽

Continuous Time ◽

Heavy Tails ◽

Tail Behavior ◽

Renewal Model ◽

Discounted Aggregate Claims ◽

Aggregate Claims ◽

Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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