Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.

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Robust stability and stabilization for singular systems with state delay and parameter uncertainty

This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.

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Robust stability and stabilization of discrete singular systems: an equivalent characterization

This technical note is concerned with the problem of designing robust static output feedback controllers for linear discrete and continuous-time systems with time-invariant polytopic uncertainties. Sufficient conditions for static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities. Furthermore, the results are also extended to H2 static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.

Static Output Feedback Control Synthesis for Linear Systems With Time-Invariant Parametric Uncertainties

https://www3.nd.edu/~vgupta2/research/publications/kmxgaaut14.pdf

On relationships among passivity, positive realness, and dissipativity in linear systems

This work investigates the problem of robust D-stability analysis for uncertain discrete singular systems with state delay and structured uncertainties. Sufficient conditions are developed to ensure that, when the nominal discrete singular delay system is regular, causal and all its finite poles are located within a specified disk, the uncertain system still preserves all these properties when structured uncertainties are added into the nominal system. A computationally simple approach is proposed and a numerical example is given to demonstrate the application of the proposed method.

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Robust D-stability analysis for uncertain discrete singular systems with state delay

Robust control analysis and design for discrete-time singular systems

A new LMI condition for robust stability of discrete-time uncertain systems

In this note, under assumptions that the nominal linear implicit system is regular, impulse-free, with all its generalized eigenvalues lying inside some specified regions, sufficient conditions are proposed to preserve the assumed properties when structured perturbations are added into the nominal system. Explicit bounds on perturbations with different structures are given in terms of the spectral radii of some nonnegative matrices. >

Robustness of regional pole placement for uncertain continuous-time implicit systems

The robustness issue of uncertain generalized state-space systems is investigated. The uncertainties, in polynomial matrix form, appear on not only the state matrix but the derivative state matrix. Based on the linear fraction transformation (LFT) technique, exact bounds of the allowable perturbations for simultaneously preserving regularity, impulse elimination, and stability can be easily obtained by checking stability of some real points only. For the stability robustness issue of generalized state-space systems subject to the considered class of uncertainties, the paper presents the most general result in the literature.

Li Lee

Papers

Robust control analysis and design for discrete-time singular systems

A new LMI condition for robust stability of discrete-time uncertain systems

Robustness of regional pole placement for uncertain continuous-time implicit systems

Robust stability of generalized state-space systems

Exact unidirectional perturbation bounds for robustness of uncertain generalized state-space systems: continuous-time cases