State-space formulation

Modularity. Since we would like to use the sufficient theory in a variety of contexts and problems, we need a theory that was easy to extend and modify depending on the context. In our state-space formulation the sufficient theory is couched in terms of constraints on variables. This theory gives us the opportunity to modularize its representation, partitioning the information necessary to prove the looseness of one type of constraint from that required to prove the looseness of a different constraint type. The ability to achieve modularity is a function not only of the theory but also of the representation, which should have sufficient granularity to support the natural partitioning of the components of the theory. 

Craig, R. R., Kurdila, A. J. and Kim, H. M. State-space formulation of multi-shaker modal analysis. Journal of Analytical and Experimental Modal Analysis 5(3) (1990), 169-183. 

R.C. Rosenberg. State-Space Formulation for Bond Graph Models of Multiport Systems. Journal of Dynamic Systems, Measurement, and Control, 93(1) 35 0. March 1971. 

The low-frequency period error remains nearly unaffected unaffected by the extended state-space formulation of the damping as illustrated by the fully drawn curve in Fig. 2b. In fact, the asymptotic behavior is given by (20) also in this case. 

The linear equation 12 can then be easily included in the state-space formulation. After operating upon the state-space equation of the extended system, i.e. that including the linearized equation, and assuming Gaussian behavior of all the responses, one obtains the following differential equation for the evolution of the covariance matrix of the responses ... 

The dynamic response analysis of an offshore tower, subjected to nonstationary ice forces, is presented for single-degree-of freedom and multi-degree-of-freedom, lumped mass, models based on evolutionary covariance matrices. The ice force excitation is idealized by i) equivalent evolutionary white noise, and ii) physical spectra. The mean square responses are computed in the time domain using the linear (state space formulation). The relationship between the physical spectrum and instantaneous spectrum analysis is discussed, and the need indicated for a study of the influence of ice force physical spectrum parameters on the response. 

A state-space formulation of the equations of motion for a linear MDOF system is useful to describe the response of both classically and nonclassically damped systems. The general (second-order) equations of motion for an -degree-of-freedom linear structure under ground excitation are in matrix form ... 

The state-space formulation of the equations of motion is also advantageous for the computation... 

The methodology to solve Eq. 34 relies on the so-called state-space formulation. According to it, Eq. 34 may be rewritten as... 

Within a structural health monitoring fi amework, the target commonly is the tracking of dynamic response, described by the general continuous state-space formulation... 

Response of Dynamic Systems to Non-Poisson Impulse Processes. State-Space Formulation... 

Palmeri A, Makris N (2008) Response analysis of rigid structures rocking on viscoelastic foundation. Earthq Eng Struct Dyn 37 1039-1063 Palmeri A, Ricciardelli F, De Luca A, Muscolino G (2003) State space formulation for linear viscoelastic dynamic systems with memory. J Eng Mech ASCE 129 715-724... 

J Eng Mech-ASCE 135(11) 1248-1256 Wagner N, Adhikari S (2003) Symmetric state-space formulation for a class of non-viscously damped systems. AIAA J41(5) 951-956... 

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