cone complementary linearization

common quadratic Lyapunov function

dynamic output feedback

linear matrix inequality

linear-quadratic regulator

linear time-invariant

multiple-input multiple-output

Markovian jump linear system

multiple Lyapunov function

single-input single-output

sliding mode control

static output feedback

switched quadratic Lyapunov functions

end of proof

end of remark

is defined as

belongs to

for all

sum

field of complex numbers

field of real numbers

field of integral numbers

space of -dimensional real vectors

space of real matrices

set of -valued continuous functions on

mathematical expectation operator

limit

maximum

minimum

supremum

infimum

rank of a matrix

trace of a matrix

minimum eigenvalue of a real symmetric matrix

maximum eigenvalue of a real symmetric matrix

block diagonal matrix with blocks

minimum singular value of a real symmetric matrix

maximum singular value of a real symmetric matrix

identity matrix with appropriate dimension

identity matrix

zero matrix with appropriate dimension

zero matrix of dimension

transpose of matrix

inverse of matrix

full row rank matrix satisfying

and

is real symmetric positive (negative) definite

is real symmetric positive (negative) semi-definite

space of square integrable functions

on (continuous case)

space of square summable infinite vector sequences

over (discrete case)

Euclidean vector norm

Euclidean matrix norm (spectral norm)

-norm: (continuous case)

-norm: (discrete case)

symmetric terms in a symmetric matrix