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Analytical expressions of the free parameters of a two-parameter stabilizing control (TPSC), solving an input/output (I/O) decoupling problem, are presented, and stability conditions are given. Multi-input-multi-output (MIMO), proper, lumped and linear time invariant (LTI) systems are considered. These systems have stabilizable and detectable realizations. The separation principle is applied to design a dynamic output control in a controller-observer feedback configuration. The I/O relation of the overall system is equivalent to a subsystem, in which the I/O decoupling problem has a solution. Also, if the state dimension of the plant is even, and is double the input dimension of the plant, then coprime factorizations of the plant used for the stabilizing controllers are proposed. The results are illustrated through an example.

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A general straightforward procedure solving the problem of algebraic loops in a bond graph model of a linear time invariant (LTI) multi-input multi-output (MIMO) system is presented. This procedure is based on a proposed junction structure and an R-field. This junction structure allows interactions only between the state variables and the dissipation field and inputs, and between the dissipation field and the co-energy variables. This junction structure decouples the elements of the dissipation field, thereby removing the algebraic loops. The outputs are only functions of the co-energy variables and the inputs. In order to obtain a physical meaning for the proposed bond graph model, the initial R-field of this bond graph is transformed to a dissipative field of 1-port resistors, transformers, and gyrators. The proposed bond graph does not have algebraic loops and allows predefined integral (BGI) or derivative (BGD) causality assignments to be realized.

Analytical expressions for the parameterization of all one-and two-degrees-offreedom stable controllers stabilizing full state information systems are presented. It is assumed that the strictly proper, lumped, and linear time-invariant nominal plant has a stabilizable realization and is strongly stabilizable, and that the number of entries of the plant state is even and is double the number of entries of the plant input. Right and left coprime factorizations of the transfer function of the plant in terms of the matrices of the plant realization are proposed, the Diophantine equation is solved, and stabilizing controllers are obtained using Youla parameterization. Conditions for strong stability are given, and the free parameters of the stabilizing controllers solving the mixed sensitivity problem are established. The results are illustrated through simulation examples of a half-car active suspension system and a two-degrees-of-freedom planar rotational robot.