SEPTEMBER 2009
Monday, September 14 - Nikita Barabanov - Stability of linear third order differential inclusions I
Abstract: For irreducible linear differential inclusions of order three the basic concepts of Lyapunov exponent and extreme norm will be introduced and explored to derive elegant necessary and sufficient conditions for asymptotic stability. The relevant analytic and algebraic reformulation of the problem will be presented and discussed.

Monday, September 21 - Nikita Barabanov - Stability of linear third order differential inclusions II

Monday, September 28 - Jayant Singh - Criteria for global asymptotic stability of multilayered recurrent neural networks (part I)
Abstract: The discrete-time multilayered Artificial Neural Networks with local feedback at each layer and a global feedback is considered. A special state space extension method is used to present corresponding equations in a form of automatic control system allowing use of criteria for absolute stability based on construction of local quadratic constraints (LQC). These LQC and corresponding linear matrix inequalities are presented and discussed. The case of system with biases in each neuron is also analyzed.

OCTOBER 2009
Monday, October 5 - Jayant Singh - Criteria for global asymptotic stability of multilayered recurrent neural networks (part II)
Abstract: The properties of special state space extension method will be described. This method affects the local quadratic constraints, and corresponding matrix inequalities will be derived. Finally, for two-layered RNN a set of linear matrix inequalities will be presented and analyzed. 

Monday, October 12 - Jayant Singh - Criteria for global asymptotic stability of multilayered recurrent neural networks (part III)

Monday, October 19 - Tayo Omotoyinbo - Absolute stability of feedback systems (part I)
Abstract: For the irreducible linear inclusions we consider properties of Lyapunov exponent and corresponding extreme norms. A numerical algorithm to compute the Lyapunov exponent for discrete time linear inclusions will be presented and discussed.

Monday, October 26 - Tayo Omotoyinbo - Absolute stability of feedback systems (part II)

NOVEMBER 2009
Monday, November 2 - Tayo Omotoyinbo - Absolute stability of feedback systems (part III)
Abstract: We consider dual linear inclusions in connection with behavior of gradients of extreme  norms along the worst case solutions. A property similar to the Pontryagin maximum principle for the case of linear inclusions will be presented and discussed.

Monday, November 9 - Tayo Omotoyinbo - Absolute stability of feedback systems (part IV)

Monday, November 16 - Tayo Omotoyinbo - Absolute stability of feedback systems (part V)

Monday, November 23 - Farhad Abdullayev - Optimal Lipschitz Extensions and Partial Differential Equations (part I)
Abstract: Motivated by the problem of finding optimal Lipschitz extensions of maps defined on the boundary of an N-dimensional domain, we introduce Aronsson's notion of absolutely minimizing Lipschitz extensions (AMLE) and we discuss its relationship with viscosity solutions of the infinity-Laplace equation.

Monday, November 30 - Farhad Abdullayev - Optimal Lipschitz Extensions and Partial Differential Equations (part II)

DECEMBER 2009

Monday, December 7 - Farhad Abdullayev - Optimal Lipschitz Extensions and Partial Differential Equations (part III)