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The optimal control law is derived for discrete-time linear stochastic systems with quadratic performance criterion and control-dependent noise. The analysis includes the study of a generalized Riccati difference equation and of the asymptotic behavior of its solutions.
Three simple nonlinear examples with physical background are considered. They illustrate how generalized state representations, which depend on time derivatives of the input, occur. It is shown with these examples how quasi-static feedback of such generalized states may be used for input–output...
We obtain necessary and sufficient conditions for the existence of strongly stabilizing solutions to Riccati equations for infinite-dimensional systems that are strongly, but not exponentially stabilizable. We apply the theory to derive a Riccati criterion for the existence of J -spectral...
The present paper studies the stability robustness problem of an uncertain state-space system. We propose a new uncertain state-space model which allows second-order uncertain parameters. The uncertainty in the model appears in the form of a combination of “additive perturbation” and...
This note proposes a frequency-domain design method to achieve an iterative learning controller for uncertain feedback control systems. For a linear time-invariant plant with multiplicative perturbations and a feedback controller, we derive a sufficient condition for the iterative process to...
A novel nonlinear control scheme—robust iterative learning control (RILC) is developed in this paper. The new robust ILC system provides a general framework targeting at synthesizing learning control and robust control methods with the help of Lyapunov’s direct method, thereafter being able...
Simple tuning formulas for the design of the PID controllers to satisfy both robustness and performance requirements are given. Robust control design is an area of intensive research. The PID formulas given in this paper are simple and can be easily adopted by the industry.
In this note, the intersample performance of linear systems, which are controlled on the basis of generalized sampled-data hold functions, in order to achieve exact model matching at the sampling instants, is analyzed. The proposed technique relies on an appropriate error system and of the...
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