Special coordinate basis for multivariable linear systems—finite and infinite zero structure, squaring down and decoupling

Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation

“…Such conditions on the triple (A, B, C) are closely related to the invertibility of the system with input λ(·) and output w(·) (actually they are sufficient conditions for invertibility [59,Theorem 3]). Other similar canonical forms have been derived by Sannuti and co-workers for the sake of control applications [58,61,62], however in this paper we shall content ourselves with the assumption of a relative degree r.…”

A multiple-derivative and multiple-delay paradigm for decentralized controller design: uniform-rank systems

“…Denote that, in the SCB, the states associated with finite invariant zero dynamics are x a (x a ∈ R n−lm ). From the development of the SCB [12] and a little algebra, it is immediate that there exists a state transformation Γ such…”

“…Specifically, we prove using the SCB that a high gain control of the above form can place the closed-loop eigenvalues into the OLHP (and in fact allow free assignment of all eigenvalues except those associated with the centralized invariant zero dynamics), assuming the plant is centrally minimum phase. From the SCB [12], the system of interest (Equation 2) has lm infinite zeros and n − lm (finite) invariant zeros. Denote that, in the SCB, the states associated with finite invariant zero dynamics are x a (x a ∈ R n−lm ).…”

“…This control architecture envisions use of one more output derivative than would be considered in the centralized case; this simple modification surprisingly allows not only stabilization but effective pole placement, for minimumphase square-invertible uniform-rank decentralized plants. We note that the Special Coordinate Basis (SCB) for linear systems [11], [12] serves as a core tool for our design, because it fully exposes both the infinite-and finite-invariant zero structure of the plant, and hence permits us to properly use the derivatives of local observations in design. From the SCB, it becomes clear that minimum-phase uniformrank plants are amenable to high-gain decentralized control, analogously to the asymptotic time-scale and eigenstructure assignment (ATEA) design for centralized systems [11], [13].…”

Properties of recoverable region and semi-global stabilization in recoverable region for linear systems subject to constraints

“…We recall from [18,20] special coordinate basis (scb) for system in (2.1). A system in scb reveals the inherent finite and infinite zero structures, which are crucial components in classifying the constraints and in facilitating the design.…”