Deterministic and stochastic linear periodic systems

Balanced Reduction of Linear Periodic Systems

“…The notion of lifted system at time k allows to analyze structural and stability properties and pole-zero structures of periodic systems [2,4,13,14]. For example, the subspace of reachable (unobservable) states of system S at time k is readily seen to coincide with that of system S L (k) if it is expressed in terms of matrices Ek> Jk> Lk and M*.…”

“…[2,12] and references therein). For this class of systems the model reduction has been analyzed using an Hankel-norm approximation and under the hypothesis of time-invariant dimension of the state-space and of time reversibility [25].…”

Discrete-Time Positive Periodic Systems With State and Control Constraints

“…its eigenvalues have modulus less than one. The following result provides other equivalent conditions for stability of system (1), see for instance [8], [9], [14].…”

Projected Generalized Discrete-Time Periodic Lyapunov Equations and Balanced Realization of Periodic Descriptor Systems

“…In the second-half of the last century, the development of systems and control theory, together with the achievements of digital control and signal processing, has set the stage for renewed interest in the study of periodic systems, both in continuous and discrete time; see, e.g., [29,54,44,12,52,14] and the survey papers [3,4]. This has been amplified by specific application demands in the aerospace realm [21,30,20], computer control of industrial processes [5] and communication systems [43,12,42,53].…”

“…The number of contributions on linear time-varying discrete-time periodic systems has been increasing in recent times; see, e.g., [15,19,22,45,47,49] and the references therein. This increasing interest in periodic systems has also been motivated by the large variety of processes that can be modelled through linear discrete-time periodic systems (e.g., multirate sampled-data systems, chemical processes, periodically time-varying filters and networks, and seasonal phenomena [2,3,7,16,28,33,51]). …”