In a previous paper, we showed how classical ideas for dynamic programming in discrete networks can be adapted to hybrid systems. The approach is based on discretization of the continuous Bellman inequality which gives a lower bound on the optimal cost. The lower bound is maximized by linear programming to get an approximation of the optimal solution. In this paper, we apply ideas from infinite...

This paper presents a new approach for determining the L2 gain of affine non-linear systems with polynomial vector fields within the sum of squares framework. The main feature of the proposed approach is that it does not require solving a Hamilton Jacobi Inequality (HJI). The solution to the HJI is done indirectly by solving another inequality augmented with slack variables. This new inequality...

• Pre-Hilbert spaces: definition • Cauchy-Schwarz-Bunyakowski inequality • Example: spaces ` • Triangle inequality, associated metric, continuity issues • Hilbert spaces, completions, infinite sums • Minimum principle • Orthogonal projections to closed subspaces • Orthogonal complements W⊥ • Riesz-Fischer theorem on linear functionals • Orthonormal sets, separability • Parseval equality, Bessel...

An important class of optimization problems in control and signal processing involves the constraint that a Popov function is nonnegative on the unit circle or the imaginary axis. Such a constraint is convex in the coefficients of the Popov function. It can be converted to a finitedimensional linear matrix inequality via the Kalman-Yakubovich-Popov lemma. However, the linear matrix inequality r...

We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the classic inequalities, a type of linear rank inequalities associated with the combinatorial structure of normal subgroups of certain matrix groups. In the 4-part...

Theorem of the alternatives for linear matrix inequality based on the separation theorems are proposed to provide systematic and unified proofs of necessary and sufficient conditions for solvability of Lyapunov inequality on P . As an application of the Theorem of the alternatives, we investigate the conditions for the existence of feasible solutions to Lyapunov inequality on P and obtain a res...

Background and Objectives: The main purpose of this study was to compare the predictive power of the Inequality-adjusted Human Development Index (IHDI) with the Human Development Index (HDI) with regard to the share of deaths caused by Non-Communicable Diseases (NCD) among all deaths in the world and Iran.   Methods: The data required for this cross-sectional ecological study were extracted f...

The continuous-and discrete-time H 1 control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems , and an LMI-based parametrization of all H 1-suboptimal controllers, including reduced-order controllers. The solvability conditions invol...

The problem of walking simulation for the quadruped search robot on a slope is described as an uncertainty system. In order to create the virtual ramp road environment, VRMLmodeling language is used to build a real environment, which is a 3D terrain scene in Matlab platform. According to the VRML model structure of the quadruped search robot, a guaranteed cost nonfragile robust controller is de...

An approach to obtaining dispersive estimates for certain multidimensional linear hyperbolic systems will be described. The key result is a local energy decay estimate which provides the intermediate link between the generalized Sobolev inequality and the energy inequality. §