We show that several system-theoretic properties are preserved under a bilinear transformation from a continuous-time linear system to a discrete-time one (and conversely). For example, strong stability, infinite-time admissibility of the control and observation operators and approximate controllability and observability are all preserved. On the other hand, exponential stability (stabilizability) is not. Moreover, we establish a 1-1 correspondence between the solutions of the discreteand continuous-time Lyapunov and Riccati equations.

BIlinear transformations between discrete- and continuouS- time infinite- dimensional linear systems

Large-scale control systems are often composed of several smaller interconnected units. For these systems, it is common to employ local controllers, which observe and act locally. At the heart of c ...

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Decentralized Control Design with Limited Plant Model Information

An approach to the decomposition and approximation of linear quadratic Gaussian control problems for singularly perturbed discrete systems at steady state is presented. The global Kalman filter is decomposed into separate reduced-order local filters through the use of a decoupling transformation. A near-optimal control law is derived by approximating coefficients of the optimal control law. The proposed method allows parallel processing of information and reduces offline and online computational requirements. A real-world example demonstrates the efficiency of the proposed method. >

Parallel reduced-order controllers for stochastic linear singularly perturbed discrete systems

The optimal solution of the weakly coupled algebraic discrete Riccati equation is obtained in terms of a reduced-order continuous-type algebraic Riccati equation via the use of a bilinear transformation. The proposed method has a rate of convergence of O( epsilon /sup 2/) where epsilon represents a small coupling parameter. A real-world physical example (a chemical plant model) demonstrates the efficiency of the proposed method. Simulation results obtained using a package for a computer-aided control system are presented. For this specific real-world example, the algorithm perfectly matches the presented theory, since convergence, with an accuracy of 10/sup -4/, is achieved after nine iterations (i.e., 0.68/sup 18/=10/sup -4/). >

Optimal reduced-order solution of the weakly coupled discrete Riccati equation

New method for optimal control and filtering of weakly coupled linear discrete stochastic systems

An interpretation of the bilinear transformation of the Riccati equation is presented. The bilinear transformation of a continuous type algebraic Riccati equation (ARE) to a discrete type ARE, and its inverse transformation, have been used for solving ARE numerically. However, its physical meaning has not been clear, and the problem formulation was complicated. This note gives a physical interpretation and derivation of the bilinear transformation of the ARE. Finally, cheap control for continuous-time linear systems is considered from the view of the bilinearly transformed system.

K. Furuta

Papers

On the bilinear transformation of Riccati equations