On Pole Placement and Invariant Subspaces

The classical eigenvalue assignment problem is revisited in this note. We derive an analytic expression for pole placement which represents a slight generalization of the celebrated Bass-Gura and Ackermann formulae, and also is closely related to the modal procedure of Simon and Mitter.Comment: Presented at ICAT201

Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cells

This paper presents a mathematical analysis on our proposed physiologically structured PDE model that incorporates multiscale and nonlinear features. The model accounts for both mutated and healthy populations of quiescent and proliferating cells at the macroscale, as well as the microscale dynamics of cell cycle proteins. A reversible transition between quiescent and proliferating cell populations is assumed. The growth factors generated from the total cell population of proliferating and quiescent cells influence cell cycle dynamics. As feedback from the microscale, Cyclin D/CDK 4-6 protein concentration determines the transition rates between quiescent and proliferating cell populations. Using semigroup and spectral theory, we investigate the well-posedness of the model, derive steady-state solutions, and find sufficient conditions of stability for derived solutions. In the end, we executed numerical simulations to observe the impact of the parameters on the model's nonlinear dynamics

Robust control of switched linear systems

Abstract-We consider robust control of switched linear systems under arbitrary time-dependent switching signals. First, we introduce a common quadratic Lyapunov function for the class of switched linear systems with Hurwitz constituent matrices in R n×n sharing n − 1 linearly independent common left eigenvectors. The common quadratic Lyapunov function is then used for robust stability analysis of the convexified differential inclusion associated with the underlying switched linear system. Finally, using the common left eigenstructure assignment approach for multi-input systems, robust design by means of state-feedback control is proposed

Data-Driven Criteria for Detectability and Observer Design for LTI Systems

We study the problems of determining the detectability and designing a state observer for linear time-invariant systems from measured data. First, we establish algebraic criteria to verify the detectability of the system from noise-free data. Then, we formulate data-driven linear matrix inequality-based conditions for observer design. Finally, we give conditions to infer the detectability of the system from noisy data.</p

Stability bounds for systems and mechanisms in linear descriptor form

Mathematical models for simulation and control of systems and mechanisms naturally arise in a descriptor form. The stability analysis of descriptor systems, involving free parameters as uncertainties or design qualifiers is subject of this paper. Two approaches for the calculation of the stability boundaries in the underlying parameter space are discussed. The first one uses a quantifier elimination method, while the second one is based on the direct solution of the Lyapunov equation. The computational methods are exemplary demonstrated on Chua’s circuit

A necessary stabilization condition for PID control

A necessary condition for the existence of a stable PID controller for a given plant is introduced. The derived rule is straightforward to check and applies generally for LTI systems, including time-continuous, time-discrete and time-delay systems. Therefore the plot of a directly constructible function is checked for a required minimal number of real zeros