Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear models. Such LTP systems can reach orders that make repeated simulation or other necessary analysis prohibitive, motivating the need for model reduction. We develo...

So just what is a Linear Time-Invariant (LTI) system, and why should you care? Systems are used to perform signal processing. The effect of a system on the spectrum of a signal can be analyzed easily if and only if the system is LTI, as we will see in these notes. The ability to design a filter to perform a specific signal processing task (e.g., filter out noise, differentiate, equalize frequen...

This paper deals with the problem of switching between several linear time-invariant (LTI) controllers—all of them capable of stabilizing a specific LTI process—in such a way that the stability of the closed-loop system is guaranteed for any switching sequence. We show that it is possible to find realizations for any given family of controller transfer matrices so that the closed-loop system re...

Bounded-input bounded-output stability conditions for fractional-order linear time-invariant (LTI) system with multiple noncommensurate orders have been established in this paper. The orders become noncommensurate orders when they do not have a common divisor. Sufficient and necessary conditions of stability for this kind of fractional-order LTI system with multiple noncommensurate orders. Base...

Most of control systems in vogue are Linear Time Invariant (LTI) systems and are characterized by several parameters such as settling time, over shoot and rise time etc. Optimization of these parameters is required to meet the desired system response and smooth operation of the system. In this paper, an optimization based compensator is designed and implemented for a closed loop LTI system and ...

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotor-bearing systems, wind turbines and nonlinear systems linearized about a periodic trajectory; all of these have been treated analytically in the literature. However, few methods exist for experimentally characterizing LTP sy...

Resilient control systems should efficiently restore control into physical systems not only after the sabotage of themselves, but also after breaking physical systems. To enhance resilience of control systems, and given an originally minimalinput controlled linear-time invariant(LTI) physical system, we address the problem of efficient control recovery into it after removing a known system vert...

AbstractIn this paper, we have characterized the discrete time single input single output (SISO) linear (L,M) shift invariant system by a two-dimensional kernel function and a filter bank structure. Based on the characterization, we have investigated the conditions for the stability, the invertibility, the causality and the finite response properties of a discrete time SISO linear (L,M) shift ...

This paper revisits the definition of linear time-invariant (LTI) stochastic process within a behavioral systems framework. Building on Willems (2013), we derive a canonical representation of an LTI stochastic process and a physically grounded notion of interconnection between independent stochastic processes. We use this framework to analyze the invariance properties enjoyed by distances betwe...

This paper extends results about stability and stabilization of a retarded quasipolynomial obtained using the Mikhaylov criterion earlier. Retarded quasipolynomials appear as numerators and denominators of linear time-invariant time-delay systems (LTI-TDS). A LTI-TDS system of retarded type (destitute of distributed delays) is said to be stable if all roots of its characteristic quasipolynomial...