On the controllability and stabilizability of linear complementarity systems

This paper studies controllability and stabilizability of linear complementarity systems that can be cast as continuous piecewise affine dynamical systems. Under a certain right-invertibility assumption, we present a la Hautus necessary and sufficient conditions for both controllability and stabilizability.</p

On Reachability and Null-Controllability of Nonstrict Convex Processes

This letter studies reachability and null-controllability for difference inclusions involving convex processes. Such difference inclusions arise, for instance, in the study of linear discrete-time systems whose inputs and/or states are constrained to lie within a convex cone. After developing a geometric framework for convex processes relying on invariance properties, we provide necessary and sufficient conditions for both reachability and null-controllability in terms of the spectrum of dual processes

Data informativity for analysis of linear systems with convex conic constraints

This letter studies the informativity problem for reachability and null-controllability of constrained systems. To be precise, we will focus on an unknown linear systems with convex conic constraints from which we measure data consisting of exact state trajectories of finite length. We are interested in performing system analysis of such an unknown system on the basis of the measured data. However, from such measurements it is only possi- ble to obtain a unique system explaining the data in very restrictive cases. This means that we can not approach this problem using system identification combined with model based analysis. As such, we will formulate condi- tions on the data under which any such system consistent with the measurements is guaranteed to be reachable or null-controllable. These conditions are stated in terms of spectral conditions and subspace inclusions, and therefore they are easy to verify

Disturbance decoupling problem for multi-agent systems:A graph topological approach

Çamlıbel, Mehmet Kanat (Dogus Author)This paper studies the disturbance decoupling problem for multi-agent systems with single integrator dynamics and a directed communication graph. We are interested in topological conditions that imply the disturbance decoupling of the network, and more generally guarantee the existence of a state feedback rendering the system disturbance decoupled. In particular, we will develop a class of graph partitions, which can be described as a "topological translation" of controlled invariant subspaces in the context of dynamical networks. Then, we will derive sufficient conditions in terms of graph partitions such that the network is disturbance decoupled, as well as conditions guaranteeing solvability of the disturbance decoupling problem. The proposed results are illustrated by a numerical example

Port-Hamiltonian Systems Theory and Monotonicity

The relationship of the theory of port-Hamiltonian systems with the mathematical concept of monotonicity is explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to systems defined with respect to maximal cyclically monotone relations, together with their generating convex functions. This gives rise to interesting subclasses of incrementally port-Hamiltonian systems, with examples stemming from physical systems modeling as well as from convex optimization. Furthermore, it is shown how cyclical monotonicity for Dirac structures is equivalent to separability. An in-depth treatment is given of the composition of maximal monotone and maximal cyclically monotone relations, where in the latter case the resulting maximal cyclically monotone relation is shown to be computable through the use of generating functions. The results on compositionality are employed for steady-state analysis and for a convex optimization approach to the computation of the equilibria of interconnected incrementally port-Hamiltonian systems. Finally, the relation to incremental and differential passivity is discussed, and it is shown how incrementally port-Hamiltonian systems with strictly convex Hamiltonians are equilibrium independent passive.</p

Port-Hamiltonian Systems Theory and Monotonicity

The relationship of the theory of port-Hamiltonian systems with the mathematical concept of monotonicity is explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to systems defined with respect to maximal cyclically monotone relations, together with their generating convex functions. This gives rise to interesting subclasses of incrementally port-Hamiltonian systems, with examples stemming from physical systems modeling as well as from convex optimization. Furthermore, it is shown how cyclical monotonicity for Dirac structures is equivalent to separability. An in-depth treatment is given of the composition of maximal monotone and maximal cyclically monotone relations, where in the latter case the resulting maximal cyclically monotone relation is shown to be computable through the use of generating functions. The results on compositionality are employed for steady-state analysis and for a convex optimization approach to the computation of the equilibria of interconnected incrementally port-Hamiltonian systems. Finally, the relation to incremental and differential passivity is discussed, and it is shown how incrementally port-Hamiltonian systems with strictly convex Hamiltonians are equilibrium independent passive.</p

Orthogonal polynomial bases for data-driven analysis and control of continuous-time systems

We use polynomial approximation theory to perform data-driven analysis and control of linear, continuous-time invariant systems. We transform the continuous-time input- and state trajectories into discrete sequences consisting of the coefficients of their orthogonal polynomial bases representations. We show that the dynamics of the transformed input- and state signals and those of the original continuous-time trajectories are described by the same system matrices. We investigate informativity, quadratic stabilization, and &lt;inline-formula&gt;&lt;tex-math notation="LaTeX"&gt;$\mathcal {H}_{2}$&lt;/tex-math&gt;&lt;/inline-formula&gt;-performance problems for continuous-time systems. We deal with the case in which machine-precision accuracy in the representation of continuous-time signals can be achieved from the data using a finite number of basis elements, and the case in which the approximation error is non-negligible.</p