Nonlinear systems analysis (2nd ed.)
Nonlinear systems analysis (2nd ed.)
Robust stabilization with positive real uncertainty: beyond the small gain theory
Systems & Control Letters
Optimal guaranteed cost control of uncertain discrete time-delay systems
Journal of Computational and Applied Mathematics
Memoryless H∞ Controllers for Discrete-Time Systems with Time Delay
Automatica (Journal of IFAC)
Technical Communique: Observer-based positive real control of uncertain linear systems
Automatica (Journal of IFAC)
Robust guaranteed cost control for a class of two-dimensional discrete systems with shift-delays
Multidimensional Systems and Signal Processing
The delay-range-dependent robust stability analysis for 2-D state-delayed systems with uncertainty
Multidimensional Systems and Signal Processing
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This paper considers the problem of positive real control for two-dimensional (2-D) discrete delayed systems in the Fornasini-Marchesini second local state-space model. Attention is focused on the design of dynamic output feedback controllers, which guarantee that the closed-loop system is asymptotically stable and the closed-loop transfer function is extended strictly positive real. We first present a sufficient condition for extended strictly positive realness of 2-D discrete delayed systems. Based on this, a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality (LMI). When the LMI is feasible, an explicit parametrization of a desired output feedback controller is presented. Finally, we provide a numerical example to demonstrate the application of the proposed method.