Stability of Quaternionic Linear Systems

Abstract

Case 2) We now wish to design the controller (6) with random communication delay = 0:1 such that the H 1 performance is minimized, i.e., we want to solve the problem P1). Solving the optimization problem (45) Similar to the first case, the simulation results of the state responses are given in Fig. 3. VI. CONCLUSIONIn this note, a novel control problem has been considered for networked systems with random communication delays. The H1 observer-based controller has been designed to achieve a desired H 1 disturbance rejection level. The controller has been obtained by solving an LMI. Simulation results have demonstrated the feasibility of our control scheme. One of our future research topics would be the design of controllers for networked systems with long random delays. vol. 34, no. 1, pp. 57-64, 1998. [14] A. Ray, "Output feedback control under randomly varying distributed delays," J. Guid., Control, Dyna., vol. 17, no. 4, pp. 701-711, 1994. REFERENCES[15] Y. Rong, "The design of H1 iterative learning control and its applica- Stability of Quaternionic Linear SystemsRicardo Pereira and Paolo VettoriAbstract-The main goal of this paper is to characterize stability and bounded-input-bounded-output (BIBO)-stability of quaternionic dynamical systems. After defining the quaternion skew-field, algebraic properties of quaternionic polynomials such as divisibility and coprimeness are investigated. Having established these results, the Smith and the Smith-McMillan forms of quaternionic matrices are introduced and studied. Finally, all the tools that were developed are used to analyze stability of quaternionic linear systems in a behavioral framework.

Infinite Matrices and Their Recent Applications

“…Moreover, A T ; A 2 HOEx n m denote the transpose and the conjugate transpose of A, respectively. More properties can be found in, for example, [87,88]. It is easy to prove that if there is a solution, then it is unique.…”

“…In [22], they studied Gröbner basis theory for the ring of quaternion polynomials and explored how to compute the module syzygy. Smith-McMillan forms of quaternion polynomial matrices are defined and some applications to dynamical systems are given in [87]. Some properties of Ore matrices can be found in [37,144].…”

Comparison of congruences and strict equivalences for real, complex, and quaternionic matrix pencils with symmetries

“…For more information and proofs, we refer the reader to [22], [23], [16], [5], [15], among many other sources. Recent interest in quaternionic linear algebra is motivated in part by applications in system and control [13], [14].…”

The Moore–Penrose inverses of matrices over quaternion polynomial rings

“…In [5], Damiano et al studied Gröbner basis theory for the ring of quaternion polynomials and explored how to compute the module syzygy. Smith-McMilian forms of quaternion polynomial matrices are defined in [22] and some applications to dynamical systems are given.…”