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

Abstract

This note 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 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.

Delay-dependent stability and stabilization criteria for T–S fuzzy singular systems with interval time-varying delay by improved delay partitioning approach

“…2002)The pair ( E ,  A ) is said to be regular if is not identically zero.The pair ( E ,  A ) is said to be impulse free if .The pair ( E ,  A ) is said to be asymptotically stable, if all roots of lie inside the unit disk with center at the origin.The delayed singular system (4) is said to be admissible if the pair ( E ,  A ) is regular, impulse free and asymptotically stable.…”

“…2002)The singular system (4) is said to be regular and impulse free if the pair ( E ,  A ) is regular and impulse free.The singular system (4) is said to be asymptotically stable, if for any , there exists a scalar such that for any compatible initial conditions, with , the solution x ( t ) of (4) satisfies for and .…”

H∞ Control of Network Control System for Singular Plant

“…Network Control System (NCS) is a distributed and a real-time feedback control system where the system node situated at different geographical position exchanges state information and control information with the controller through a communication network [20]. Network bandwidth and restraint of communication mechanism such as network delay and data packet loss exist typically in network communication channel, which makes NCS loses invariability, integrality, causality and certainty [18], and due to this fact the study of NCS is more complicated and challenging.…”

An efficient observer design method for singular discrete-time systems with time-delay and nonlinearity: LMI approach

“…The singular systems are used to describe many practical applications such as robotic systems, biological systems, electrical networks, economic systems, social systems, constrained mechanical systems, space navigation systems, chemical processing, astrophysics, aircraft modelling, etc. [1][2][3][4][5][6]. Over the past years, the control problem of these classes of systems has been widely studied, and many researches, such as feedback control [7], robust H 1 control [8,9], optimal control [10], impulsive control [11], sliding mode control [12], passive control [13], and fault-tolerant control [14], have been investigated in this eld.…”