This article deals with the design of quadratic and linear dynamic output feedback controllers for systems to ensure, on one hand, local exponential stability origin in closed-loop form and, other increase an estimate basin attraction as large possible. The introduction a term controller allows us consider same class dynamics studied system. Here, our approach is Lyapunov function respect exten...

This paper focuses on the problems of a diagonal common quadratic Lyapunov function (DCQLF) existence for sets of stable positive linear time-invariant (LTI) systems. We derive the equivalent algebraic conditions to verify the existence of a DCQLF, namely that the finite number Hurwitz Mezler matrices at least have a common diagonal Stein solution. Finally some reduced cases are considered. 201...

It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. It is also well known that this mapping preserves common quadratic Lyapunov functions between continuous-time and di...

A new test of robust stability/performance is proposed for linear systems with uncertain real-valued parameters. This test is an extension of the notion of quadratic stability where the xed quadratic Lyapunov function is replaced by a Lyapunov function with aane dependence on the uncertain parameters. Admittedly with some conservatism , the construction of such parameter-dependent Lyapunov func...

This paper presents new tests to analyze the robust stabilityand/or performance of linear systems with uncertain real parameters.These tests are extensions of the notions of quadratic stability andperformance where the fixed quadratic Lyapunov functionis replacedby a Lyapunov functionwith affine dependence on the uncertain pa-rameters. Admittedly with some conservati...

State-space stability of linear shift-invariant discrete two-dimensional (2-D) dynamics is considered. An approach to the making of Lyapunov functions for 2-D dynamics is presented. It produces quadratic forms involving finite cross-terms among local states. The scope of the stability analysis based upon the notion of parallel stability expands, and the accuracy can be improved by this approach.

Recently a large number of literature on fuzzy control are TS model-based control where, mostly, the common P approach searching for a single Lyapunov function remains active Wang et al. [1996], Tanaka et al. [1998], Kim and Lee [2000], Blanco et al. [2000], Tuan et al. [2001]. Another category emphasizes parameter-dependent functions with multiple Pj matrices as a candidate of Lyapunov functio...

Suppose that A and B are real stable matrices, and that their difference A − B is rank one. Then A and B have a common quadratic Lyapunov function if and only if the product AB has no real negative eigenvalue. This result is due to Shorten and Narendra, who showed that it follows as a consequence of the Kalman-Yacubovich-Popov solution of the Lur’e problem. Here we present a new and independent...

We present efficiently verifiable sufficient conditions for the validity of specific NPhard semi-infinite systems of linear matrix inequalities (LMIs) arising from LMIs with uncertain data and demonstrate that these conditions are “tight” up to an absolute constant factor. In particular, we prove that given an n × n interval matrix Uρ = {A | |Aij − Aij | ≤ ρCij}, one can build a computable lowe...