Kan Tan

Stabilization and H ∞ control of symmetric systems: an explicit solution

Abstract In this paper we address the H ∞ control analysis, the output feedback stabilization, and the output feedback H ∞ control synthesis problems for state-space symmetric systems. Using a particular solution of the Bounded Real Lemma for an open-loop symmetric system we obtain an explicit expression to compute the H ∞ norm of the system. For the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state-space symmetric systems. For the H ∞ control synthesis problem we derive an explicit expression for the optimally achievable closed-loop H ∞ norm and the optimal control gains. Extension to robust and positive real control of such systems are also examined. These results are obtained from the linear matrix inequality formulations of the stabilization and the H ∞ control synthesis problems using simple matrix algebraic tools.

State-feedback control of LPV sampled-data systems

In this paper, we address the analysis and the state-feedback synthesis problems for linear parameter-varying (LPV) sampled-data control systems. We assume that the state-space data of the plant and the sampling interval depend on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. We explore criteria such as the stability, the energy-to-energy gain (induced L2 norm) and the energy-to-peak gain (induced L2 -to- L∞ norm) of such sampled-data LPV systems using parameter-dependent Lyapunov functions. Based on these analysis results, the sampled-data state-feedback control synthesis problems are examined. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities that can be solved via efficient interior-point algorithms.

Robust decentralized control using an alternating projection approach

Provides a geometric formulation of the robust decentralized control problem for both continuous-time and discrete-time systems. The problem is formulated as a feasibility problem of finding a set of matrix parameters in the intersection of a set of linear matrix inequalities (LMIs) and a non-convex rank constraint. Alternating projection methods are proposed for solution. Fixed-order, interval and structural constraints can be imposed on the controller in the same framework.

Output-feedback control of LPV sampled-data systems

In this paper, we address the output-feedback synthesis problems for linear parameter-varying (LPV) sampled-data control systems with potentially variable sampling rates. We assume that the state-space matrices of the plant and the sampling interval depend on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. The sampled-data output-feedback control synthesis problems are examined for criteria such as the energy-to-energy gain (induced L/sup 2/ norm) and the energy-to-peak gain (induced L/sup 2/-to-L/sup /spl infin// norm) using parameter-dependent Lyapunov functions. The synthesis conditions are formulated in terms of linear matrix inequalities (LMI) that can be solved via efficient interior-point algorithms.

Stabilization and H∞ control of discrete-time symmetric systems

We examine the H^∞ control analysis, the output feedback stabilization, and the output feedback H^∞ control synthesis problems for discrete-time state-space symmetric systems. We obtain explicit analytical solutions for the H^∞ norm of such systems, and an explicit parametrization of the output feedback stabilizing controllers and H^∞ controllers. Extensions to robust and positive real control of such systems are also examined. These results are obtained from the linear matrix inequality formulations of the stabilization and the H^∞ control synthesis problems for discrete-time systems using simple matrix algebraic tools. The results have obvious computational advantages, especially for large scale symmetric systems.

L/sub 2/-L/sub 2/ and L/sub 2/-L/sub /spl infin// output feedback control of time-delayed LPV systems

We examine the analysis and output feedback synthesis problems for linear parameter-varying (LPV) systems with parameter-varying time delays. It is assumed that the state-space data and the time delays are dependent on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. We explore the stability, the L/sub 2/ induced norm performance and the L/sub 2/-to-L/sub /spl infin// gain performance of these systems using parameter-dependent Lyapunov-Krasovskii functionals. In addition, the designs of parameter-dependent dynamic output feedback controllers that guarantee stability and desired induced norm performance are examined. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities (LMI) that can be solved via efficient interior-point algorithms.