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.

In this paper we study behavioral systems whose trajectories are given as solutions of quaternionic difference equations. As happens in the commutative case, it turns out that quaternionic polynomial matrices play an important role in this context. Therefore we pay special attention to such matrices and derive new results concerning their Smith form. Based on these results, we obtain a characterization of system theoretic properties such as controllability and stability of a quaternionic behavior.

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In this paper we study the representation of periodically time-varying convolutional codes by means of periodic input-state-output models. In particular, we focus on period two and investigate under which conditions a given two-periodic convolutional code (obtained by alternating two time-invariant encoders) can be represented by a periodic input-state-output system. We first show that one cannot expect, in general, to obtain a periodic input-state-output representation of a periodic convolutional code by means of the individual realizations of each of the associated time-invariant codes. We, however, provide sufficient conditions for this to hold in terms of the column degrees of the associated column reduced generator matrices. Moreover, we derive a sufficient condition to obtain a periodic statespace realization that is minimal. Finally, examples to illustrate the results are presented.

SUMMARYIn this paper we propose a definition of determinant for quaternionic polynomial matrices inspired by the well-known Dieudonné determinant for the constant case. This notion allows to characterize the stability of linear dynamical systems with quaternionic coefficients, yielding results which generalize the ones obtained for the real and complex cases.