In this paper, a new approach for the stability analysis of continuous-time Takagi–Sugeno (T-S) fuzzy system is proposed. The universe set is divided to subregions, and piecewise quadratic Lyapunov function is then found for each of them. This class of Lyapunov function candidates is much richer than the common quadratic Lyapunov function. By exploiting the piecewise continuous Lyapunov functio...

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.

The paper establishes the design procedure for the state feedback control of linear discrete-time systems, considerable as an interposed design criterium in the form of linear matrix inequalities. The goal is to design the feedback control which guarantees bounded H2 performance index for the system transfer function matrix and H∞ norm attenuation for the disturbance transfer function matrix, b...

For both discrete-time and continuous-time linear multi-variable control systems, we introduce a concept of control Lyapunov modes associated with a control Lyapunov function in a quadratic form. We prove that the number of unstable control Lyapunov modes is at most equal to the number of input of the system.

We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switc...

In this work we deal with global stability properties of classic SIS, SIR and SIRS epidemic models with constant recruitment rate, mass action incidence and variable population size. The usual approach to determine global stability of equilibria is the direct Lyapunov method which requires the construction of a function with specific properties. In this work we construct different Lyapunov func...

We propose the notion of nondecreasing Lyapunov functions which can be used to prove stability or other properties of the system in question. This notion is in particular useful in studying switched or hybrid systems. We illustrate the concept by a general construction of such a nondecreasing Lyapunov function for a class of planar hybrid systems. It is noted that this class encompasses switche...