We present a numerical method to compute the SVD-like decomposition B = QDS−1, where Q is orthogonal, S is symplectic and D is a permuted diagonal matrix. The method can be applied directly to compute the canonical form of the Hamiltonian matrices of the form JBTB, where J = [ 0 −I I 0 ] . It can also be applied to solve the related application problems such as the gyroscopic systems and linear...

The behavior of the rightmost characteristic roots of linear time-delay systems as a function of the delay parameter is studied for small values of a gain parameter. The results explain the qualitative behavior of the stability regions in the delay parameter space of oscillatory systems subjected to large delays, and shed a new light on the corresponding stabilization problem. In particular, fo...

Inertially stabilized platforms are subject of interest for different application, e.g. telecommunications, robotics and military systems. In this paper the objective is to maintain the line-of-sight constant despite the motion of a host vehicle. The platform stabilization problem is addressed using dual-axis gyroscopic sensors, where certain vehicle dynamic constraints are considered. Sensor p...

Observers are widely used to generate residuals for fault diagnosis processes. However the generated residuals are not only influenced by faults but also by disturbances and model uncertainties. In order to avoid false alarm and achieve a high fault detection rate disturbances and model uncertainties have to be considered in the fault detection and isolation (FDI) processes. In rotor systems th...

A class of symmetric static output feedback controllers are known to robustly stabilize symmetric collocated second-order linear time invariant systems having positive definite or positive semi-definite coefficient matrices. This paper extends the result to the asymmetric systems which include skew-symmetric gyroscopic terms. We first obtain the condition for static output feedback controllers ...

This manuscript introduces a passivity-based integral control approach for fully-actuated mechanical systems. The novelty of our methodology is that we exploit the gyroscopic forces systems to exponentially stabilize system at desired equilibrium even in presence matched disturbances; additionally, show robust against unmatched disturbances. Furthermore, provide tuning rules prescribe performan...

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n,Λ = diag{λ1, · · · , λp} ∈ Cp×p, X = [x1, · · · , xp] ∈ Cn×p, where p < n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ̄2j−1 ∈ C, x2j = x̄2j−1 ∈ C for j = 1, · · · , l, and λk ∈ R, xk ∈ R for k = 2l+1, ...

Wearable projectors have been extensively studied with a focus on miniaturization. However, stabilization of the projected images is critical, for otherwise the information cannot be read when the user walks or runs. This paper introduces two methods of stabilization for images projected on the user’s hand: optical stabilization and gyroscopic stabilization. We conducted an experiment to quanti...