Understanding the Difference Between Robust Control and Optimal Control in a Linear Discrete-Time System with Time-Varying Parameters

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

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Adaptive robust control scheme for linear systems with unknown time-varying parameters

The second international conference on computing anticipatory systems, CASYS’98 ◽

10.1063/1.58278 ◽

1999 ◽

Author(s):

Midori Maki ◽

Kojiro Hagino

Keyword(s):

Robust Control ◽

Linear Systems ◽

Adaptive Robust Control ◽

Time Varying ◽

Varying Parameters ◽

Control Scheme ◽

Time Varying Parameters

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Further Results on Reachable Set Bounding for Discrete-Time System with Time-Varying Delay and Bounded Disturbance Inputs

Complexity ◽

10.1155/2018/9259284 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11

Author(s):

Wei Kang ◽

Hao Chen ◽

Kaibo Shi ◽

Jun Cheng

Keyword(s):

Discrete Time ◽

Sufficient Conditions ◽

Reachable Set ◽

Time Varying ◽

Discrete Time System ◽

Initial State ◽

Time System ◽

Time Varying Delay ◽

Bounded Disturbance ◽

Varying Delay

This paper investigates the problem of reachable set bounding for discrete-time system with time-varying delay and bounded disturbance inputs. Together with a new Lyapunov-Krasovskii functional, discrete Wirtinger-based inequality, and reciprocally convex approach, sufficient conditions are derived to find an ellipsoid to bound the reachable sets of discrete-time delayed system. The main advantage of this paper lies in two aspects: first, the initial state vectors are not necessarily zero; second, the obtained criteria in this paper do not really require all the symmetric matrices involved in the employed Lyapunov-Krasovskii functional to be positive definite. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

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