Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabil...

The following matrix equations: ATXB+ BTXTA = C and ATXB+ BTXA = C, are encountered in many systems and control applications, and these matrix equations contain several linear matrix equations as special cases. In the present work, we introduce the inequalities for the determinant of the solutions of these matrix equations, separately. Then using these inequalities, we introduce a lower bound f...

Recent results by the authors have shown how to construct a class of structured controllers for large scale spatially interconnected systems via linear matrix inequalities. Of paramount importance in the control of interconnected systems is that the controlled system be stable when arbitrarily small communication delays are present between subsystems. In this paper, it is shown how to realize t...

We give linear-inequalities-based sufficient conditions for the unsolvability and solvability of the NP-hard absolute value equation (AVE): Ax − |x| = b, where A is an n × n square matrix. The satisfaction of the linear inequalities is easily verified using a linear program.

In this article we provide a solution to the mixed H 2 =H 1 problem with reduced order controllers for time-varying systems in terms of the solvability of diierential linear matrix inequalities and rank conditions, including a detailed discussion of how to construct a controller. Immediate specializations lead to a solution of the full order problem and the mixed H 2 =H 1 problem for linear sys...

Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, terms Linear Matrix Inequalities and Bilinear Inequalities.

The problems of robust stability for a class of the polytopic-type uncertain singular stochastic systems with time-varying delays are studied. By using a delay decomposition approach and terms of linear matrix inequalities (LMIs), robust stability criteria ensuring globally stochastically asymptotic stability of the polytopic-type uncertain singular stochastic systems with time-varying delays a...

Although model reference adaptive control has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, an linear matrix inequalities-based hedging approach is developed and evaluated for model re...