<inline-formula> <tex-math notation="TeX">${\cal H}_{\infty}$</tex-math></inline-formula> and <inline-formula> <tex-math notation="TeX">${\cal H}_{2}$</tex-math></inline-formula> Norms of 2-D Mixed Continuous-Discrete-Time Systems via Rationally-Dependent Complex Lyapunov Functions

H∞ and H2 Norms of 2-D Mixed Continuous-Discrete-Time Systems via Rationally-Dependent Complex Lyapunov Functions

This paper addresses the problem of determining the H∞ and H2 norms of 2D mixed continuous-discrete-time systems. The first contribution is to propose a novel approach based on the use of complex Lyapunov functions with even rational parametric dependence, which searches for upper bounds on the sought norms via linear matrix inequalities (LMIs). The second contribution is to show that the upper...

Euler's Formula via Potential Functions

A new proof of Euler's formula for polytopes is presented via an approach using potential functions. In particular, a connection between Euler's formula and the Morse relation from differential topology is established.

Math 254a: the Analytic Class Number Formula, and Dirichlet Characters

Formula Layout Formula Layout

Both the quality of the results of TEX s formula layout algorithm and the complexity of its description in the TEXbook are hard to beat The algorithm is verbally described as an imperative program with very complex control ow and complicated manipulations of the data structures representing formulae In a forthcoming textbook we describe TEX s formula layout algorithm as a functional program tra...

On the H-Infinity Norm of 2D Mixed Continuous-Discrete-Time Systems Via Rationally-Dependent Complex Lyapunov Functions

This paper addresses the problem of determining the H∞ norm of 2D mixed continuous-discrete-time systems. A novel approach is proposed based on the use of a class of complex Lyapunov functions with rational dependence on a parameter, which provides upper bounds on the sought norm via linear matrix inequalities (LMIs). It is also shown that the provided upper bounds are nonconservative by using ...