Simultaneous controller design for linear time-invariant systems

Abstract

APPENDIXLemma A: Let C be a q x n matrix and 9 any subspace of f such that Y n Ker C = 0 ; then there exist matrices L , and L , satisfying L , C + L, = I, Ker L , = Y . Lemma B: Let B be an n x p matrix, and Y any subspace of f such that 2' + Im B = Y" ; then there exist matrices L , and L , satisfying BL, + L , = I, Im L , = 2 .For brevity, we do not give the proofs. REFERENCESH. Imai and H. Akashi, "Disturbance localization and pole shifting by dynamic compensation," IEEE Trans. Automat. Revisiting the regulator problem in the geometric approach-Part I: Disturbance localization by dynamic compensation," J . Optimiz. Theory Appl., vol. 53, no. 1, pp. 9-22, 1987. J. C. Willems and C. Commault, "Disturbance decoupling by measurement feedback with stability or pole placement," SIAM J . Contr.Abstract-This note studies the use of generalized sampled-data hold functions (GSHF) in the problem of simultaneous controller design for linear time-invariant plants. This problem can be stated as follows.Given plants P , , P z , e.., PN, find a controller C which achieves not only simultaneous stability, but also simultaneous optimal performance in the N given systems. By this, we mean that C must optimize an overall cost function reflecting the closed-loop performance of each plant when it is regulated by C. Applying GSHF to the simultaneous design problem, we give solutions in three aspects: simultaneous stabilization, simultaneous optimal quadratic performance, and simultaneous pole assignment in combination with simultaneous intersampling performance.Abstract-Given a family of real nth-order polynomials P , the spectral set of P is defined as U ( @ ) A { z e~: p ( z ) = O f o r s o m e p ( . ) E B } . The focal point of this note is the problem of generating the spectral set for two different families of polynomials P-spherical families and polytopic families. For the spherical case, a closed form equation describing the boundary of the spectral set is obtained. In the polytopic Manuscript

Simultaneous pole assignment by multi-structured multirate sampled-data controllers—orthogonality consideration

“…1oxi*12*'1* 7 Methods of simultaneous stabilization using non-conventional sampled-data controllers can be classified into two types. The method of the first type10-'2.7 attains simultaneous stabilization as follows: first design a deadbeat controller Cj for each Pi, and then make a single time-varying controller C by switching the control law from C, to Ch in turn while each law is kept longer than its settling time.…”

Parallel simultaneous stabilization of a set of Port-Controlled Hamiltonian systems subject to actuator saturation

“…It is noted that this kind of stabilization is different from the traditional simultaneous stabilization problem [21−22] . The traditional simultaneous stabilization problem is one of important research topics in the area of robust control and has received a considerable attention in the past few decades, see, e.g., [21][22][23][24][25][26]. Recently, the PSS problem was investigated in [27] for Hamiltonian systems, and some interesting results were obtained for the existence of PSS controllers of a set of Hamiltonian systems.…”

Generalized sampled‐data hold functions for robust multivariable tracking and disturbance rejection

“…If a sampled-data system is controllable, the e!ect of output injection can be realized by periodic output feedback see References [1}4]. Periodic output feedback for simultaneous controller design has been studied in Reference [5], where the periodic feedback gain is referred to as generalized sampled-data hold function: output samples are multiplied by a time-varying hold function and fed back to the plant input. What normally prevents this type of controller from being applied in practice is its tendency to produce strong oscillation between output sampling instants.…”