This paper introduces a linear state-space model with timevarying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights in the linear combination is modelled by another linear Gaussian dynamical model allowing the model to learn how the dynamics of the process changes. Previous...

We consider a discrete-time, linear time varying (LTV), multiple input, multiple output (MIMO) system with nu inputs and ny outputs. The system is known to be asymptotically stable, but the exact dynamics and the way they change over time are not known. We denote the vector of control inputs at time step t ∈ Z by u(t) = [u1(t), . . . , unu(t)] T , where ui(t) ∈ R, i = 1, . . . , nu are the indi...

Flutter-induced vibrations can easily cause large structures like airplanes and bridges to fail, which even today makes flutter prediction an important topic of research. To predict flutter, recursive system identification can be used to capture the time-varying behavior using timeinvariant techniques combined with the forgetting of old data. However, forgetting older data takes time, which int...

A strategy is proposed to model the complex industrial systems using linear time-varying system (LTV S). The proposed methodology is independent of model structure and the model may take any classic linear structure such as finite impulse response, input-output relation structures etc. To take into account the error between system and model due to model order reduction, variation of system beha...

A strategy is proposed to model the complex industrial systems using linear time-varying system (LTV S). The proposed methodology is independent of model structure and the model may take any classic linear structure such as finite impulse response, inputoutput relation structures etc. To take into account the error between system and model due to model order reduction, variation of system behav...

This paper treats model reduction of linear time-varying models in continuous time. The method proposed is based on time-varying Lyapunov inequalities and balancing of Gramians. An error bound for truncated models that generalizes the well-known ’twicethe-sum-of-the-tail’-formulafor time-invariant balanced systems is obtained. Input-output stability of truncated balanced models is also proved.

This paper applies a model reduction method for linear parameter-varying (LPV) systems based on parameter-varying balanced realization techniques to a body freedom flutter (BFF) vehicle. The BFF vehicle has a coupled short period and first bending mode with additional structural bending and torsion modes that couple with the rigid body dynamics. These models describe the BFF vehicle dynamics wi...

A time-varying autoregressive model with time-varying coefficients is introduced in this paper for parameter extraction from non-stationary vibration signals. With this model, the relationship between linear time-varying modal parameters, i.e., instantaneous frequencies and damping factors, and time-varying autoregressive model coefficients is established. The time-varying autoregressive modeli...

The notion of properness, well-known for constant linear systems, is generalized to the time-varying case. In a module theoretic framework intrinsic characterizations of input-output system properness are derived. For this, ltrations and the associated Hilbert polyno-mials are used. Classical criteria for properness of polynomial and state representations for constant linear systems are general...